Report No. UMICH 014571-17-I The University of Michigan Department of Mechanical Engineering Cavitation and Multiphase Flow Laboratory Investigation of Secondary Liquid Phase Droplet Accelerations written by: J. J. Margle Supported by: National Science Foundation Grant No. ENG 75-2315 and U-N internal (SEP) funds. April 1978

Introduction Due to less scheduled maintenance and the increased cost of downtime, turbine blade errosion (Fig. 1) [1] has become an important consideration in the design of low pressure stages of todays steam turbines. Krzyzanowski [7] has estimated turbine blade errosion for a small system (500 kw) can be as costly as $1000/kw over the 40 year life of the system. Such economic considerations have motivated the study of turbine blade errosion. This investigation deals with the motion of secondary droplets in a steam wake behind a stationary turbine blade. Such secondary droplets result from a thin liquid film which forms on the stationary blade due to the accumulation of primary droplets. The main stream steam flow causes this liquid film to break up at the trailing edge of the blade resulting in the formation of secondary droplets. As these droplets leave the trailing edge they are accelerated into the main stream steam wake. This acceleration was observed experimentally and the results are presented. Analytical prediction of droplet acceleration based on drag considerations is also attempted. Figure 2 depicts the experimental apparatus while Figure 3 [8] shows its operation schematically. Statistical approach is also attempted using a least squares regression analysis. Numbers in brackets designate References at end of paper.

-2 -Discussion of Results Experimental secondary droplet accelerations were obtained from the observation of high speed motion pictures of the trailing edge of the stationary blade. Droplet size and position from the trailing edge were recorded for the steam velocities and liquid film flows shown in tables 1 and 2. Once knowing the droplet position and the motion picture film speed of 5000 frames per second, the velocity (ld U - l /~At ) and the acceleration ( ad J Z Lt ) were easily calculated. This reduction of data (droplet position as a function of time) was accomplished through the use of a digital computer program [6]. Average accelerations for the flow conditions outlined above are also listed in tables 1 and 2 and shown graphically in Figure 4. These average accelerations were based on the arithmetic average of all those droplets observed for each liquid film flow rate. Analytical prediction of droplet acceleration was based upon the following considerations: 1) the droplet after leaving the trailing edge assumed a spherical shape. 2) the main stream steam was one dimensional steady flow. 3) the main stream steam velocity is much larger than the droplet velocity, Ud. *D Hence, BUr — s -d 4) the main stream steam density, i5, and the droplet density,, remain constant. 5) Drag force has an overwhelming influence on the droplet acceleration. See Figure 5. From (5) above it follows d t

-3 -noting, - '7/+"J9-/ and " also, V2odJ - ~ d Rearranging and substituting into equation (1) yields the following working equation, (Droplet acceleration) J L C 3 75 3 where CD is taken from [4] as d CD =24 (1 + 0.17 R) D R e This resulted in CD values that agreed with [5] within 2-20% for the range of Reynolds' numbers encountered. Density of the water droplet was taken to be constant, Jd = 1.0 gm/cm3 (62.4 lbm/ft3). The density of the steam was also taken to be constant and equal to that of saturated steam at 2.5 psia and 134.4 F. namely, F = 1.135 x 104 gm/cm (7.086 x 103 lbm/ft ). Analytically calculated droplet accelerations have been calculated for each droplet observed; however, only the average analytical accelerations for each liquid film flow are shown in tables 1 and 2 and Figure 4. Observing the ratio of experimental acceleration to analytical acceleration, as shown in tables 1 and 2, one finds this ratio to be less than 1.0 for the 305, 525 and 1100 steam velocities. This would be expected since the analytical model considers only drag effects and should tend to predict accelerations larger than those observed. For the 825 and 975 steam velocities one notices this ratio to fluctuate about 1.0. This suggests some phenomenon in addition to simple drag considerations. Perhaps the steam velocity profile just past the trailing edge of the fixed blade is such that vortices are created. These vortices

-4 -may tend to increase or retard the droplet accelerations depending on the droplets' initial position relative to the center of the vortex. In any case, caution should be exercised when reviewing the results of the higher steam velocities. For example, one notices the observed accelerations for the 825 ft/sec run to be double those of the 520 ft/sec run. This means that while studying every fifth frame of the high speed motion pictures, a droplet would traverse the width of the frame in one half the time or in one half the number of frames observed. Hence one would obtain nearly one half the number of raw data points. Consequently, the experimentally observed acceleration for these cases is less likely to be as precise a measure of true droplet acceleration. Perhaps a study of every second frame may result in a more accurate droplet acceleration at large steam velocities. Figure 4 does show the droplet accelerations to be essentially independent of liquid film flow for the lower steam velocities. However, it is apparent that droplet accelerations do increase with increasing steam velocity.

Statistical Considerations Due to the nature of the physical phenomenon under consideration and due to the large amount of experimental data collected, certain statistical tools can be used to better understand the experimental results. The first approach was to perform a multivariate regression analysis using the MIDAS [3] package of statistical programs. This multivariate approach is shown schematically in figure 6. Specific results are contained in Appendix A. These results lead to the more meaningful first order regression analyses of experimental droplet acceleration-., E.A., on flow rate, Q, and experimental droplet acceleration, E.A., on steam velocity, v JS Table 3 summarizes the results of a first order regression analysis of E.A. on Q. Here we see an equation of the form E.A. = AL(Q) + b where, E.A. = experimental droplet acceleration Al = slope b = "y" intercept Table 3 shows the slope _1~ not to be significantly different than zero slope in -the cases out of five. This indicates "flat" or level lines on plots of E.A. vs. Q (see Figure 4). R-SQR or "goodness of fit" parameter bears this out in the same three cases, in that, it says only a very small percentage of the variation in E.A. is explained by a variation in Q. Hence one can conclude, in a statistical sense, that E.A. is not affected by Q. Since the slopes can be considered statistically equal to zero, the intercepts, b, then become some indication of an "average" acceleration for a given steam velocity irrespective of flow rate. The statistically average values shown in table 3

-6 -compare favorably with those shown in table 1. S.E. values shown in table 3 are an estimate of standard error or standard deviation of E.A. about the regression line shown in Figure 4. Hence if 2*(S.E.) lines (2T-bands) are drawn above and below the respective regression lines, 95.4% of the E.A.'s would lie within the bands. When considering a first order regression analysis of E.A. on T1;5 one must consider the relationship shown in equation (2), namely d L d d (2-) taking the square root of both sides, Equation (3) shows ~d. to be a linear function of -LS, hence a transformation of the experimental acceleration data is required in order to perform the most meaningful first order regression of E.A. on UTS. Table 4 shows resultant E.A. data while table 5 and Figure 7 show results of the regression analysis. Again, one notices an equation of the form 4.iF.- =MLTs) + b where: 4.A. = square root of experimental droplet acceleration A'~ = slope b = "y" intercept = zero In this case all the slopes we found to be statistically different than zero. Goodness of fit, R-SQR shows, for the Q = 17.7 case, 76..1% of variation in ~JE.A. can be explained by the variation in 4TS, which indicates E.A. to be a strong function of 1C3~ (as is indicated by equation (2)). Intercept, b, equal zero, i.e., E.A. = O at 5 = O. Makes sense, no droplets are being accelerated when there is no steam flow. The slope Ma corresponds to the term in

-7 -brackets in equation (3), hence substituting the following known quantities at Q = 35.3 x 10 5 ft3/min and LkJ = 305 ft/sec2 R = 1036 e CD = 24 + 0.17 (R 667 0.4265 e d = 0.003281 ft d = 62.4 lbm/ft3 s =.007086 lbm/ft3 ) CD 3, 3 b = (0.4265) (.007086) (3) = 0.1052 D -d 4d (62.4) (4) (.00328) Note 0.1052 compares favorably with the statistically obtained slopes shown in table 5. Also S.E. or standard error is an estimate of the standard deviation about the regression line shown in Figure 7. The two conditions (Q = 10 and 20) are representative of the remaining data.

-8 -Conclusions 1. Droplet accelerations are unaffected by liquid film flow for steam velocities of 500 ft/sec or less. 2. The absolute magnitude of droplet acceleration does increase with increasing steam velocity. 3. Equation (2) may be used to predict the magnitude of droplet accelerations for 305 4 U 1100 feet per second. 4. First order statistical regression analysis supports all of the above conclusions.

-9 -List of Symbols UL - velocity 1 - density Vj - segression slope - mass b - regression intercept CD - drag coefficient A - crossectional area f - volume a - acceleration E.A. - average experimentally observed droplet acceleration A.A. - average analytical droplet acceleration d - droplet R - Reynolds number e XA - change in, as, A nL-change in velocity Q - liquid film flow rate t - time Subscripts d - droplet s - steam r - relative, as in relative velocity T,

-10 -Acknowledgements Special thanks go to: 1) Mr. R. Niedzielski for his diligent work in obtaining raw data by reviewing all the high speed motion pictures. 2) Mr. M. Wegenka for his excellent work in developing a digital computer program to reduce the raw data. 3) Professor F. G. Hammitt and Mr. W. Kim for their guidence and many helpful suggestions.

-11 -References 1. Christie, D. G., et. al. "The Formation of Water Drops Which Cause Turbine Blade Erosion," The Institution of Mechanical Engineers, London, April 13-15, 1966. 2. Lipson, Charles and Sheth, N.J., Statistical Design and Analysis of Engineering Experiments, McGraw - Hill Book Company, New York, 1973. 3. Staff of Statistical Research Laboratory, Elementary Statistics Using MIDAS - User's Manual, Second Edition, The University of Michigan, Ann Arbor, MI, December, 1976. 4. Serafini, J. S., Impingement of Water Droplets on Wedges and Diamond Airfoils at Supersonic Speeds, National Advisory Committee for Aeronautics, Technical Note 2971, 1953. 5. Sabersky, Acosta and Haystmann, Fluid Flow - A First Course in Fluid Mechanics, Second Edition, MacMillan Publishing Co., 1971. 6. Wegenka, M., Multiphase Flow and Cavitation Computer Analysis Programs, The University of Michigan Department of Mechanical Engineering, UMICH No. 014571-11-I, Dec. 1977. 7. Krzyzanowski, J., Erosion Problem of High Performance Steam Turbine, Seminar - University of Michigan Cavitation and Multiphase Flow Laboratory, Nov. 1977. 8. Krezeczkowski, S., et. al., Investigations of Secondary Liquid Phase Structure in Steam Wake, University of Michigan Department of Mechanical Engineering,.UMICH No. 014571-1-T, June, 1976 (Mod. 2, April, 1977).

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Appendix - A "MIDAS Results" Due to the nature of the physical phenomenon under consideration and due to the large amount of experimental data collected certain statistical tools were used to better understand the experimental results. Reduction of the initial raw data [6] resulted in 855 droplet accelerations for the flow condition outlined in tables 1 and 2. These 855 cases were broken into 327 subsets for which average droplet accelerations were obtained. (Do not confuse the average accelerations mentioned here with those shown in tables 1 and 2. Tables 1 and 2 data are average accelerations from the "855" dataset for each specific flow condition, i.e., for -5 3 = 305 ft/sec and Q = 17.7 x 10- ft/min 2 average E.A. = 838 ft/sec is an average of the "855" dataset). When performing a first order regression of E.A. on Q the 327 dataset was arranged into the following cases corresponding to constant steam velocity, U[~S, and stored on data file "AVGACCEL": Cases TL S(ft/sec) 1-45 305 46-129 520 130-185 825 186-246 975 247-327 1100 In a similar manner the "327" dataset was rearranged in order to perform a first order regression of *IE.A. on.JTS with liquid water film flow, Q, bein~ held constant.

*A-2* Cases Q (cm3 min) 1-3 0 4-58 5 59-130 10 131-198 15 199-250 20 251-294 30 295-302 40 303-327 50 Note, these data were stored on data file "QACCEL." MIDAS "REGRESSION" command was used to perform the regression analyses refered to throughout the text. These results can be found between the heavy dark lines on the attached output. Under "Regression" of E.A. on Q at constant <T, for g = 520 ft/sec the various important output parameters are noted. Consult MIDAS user's manual [3] concerning details of other output parameters or other MIDAS commands.

> 250 12549.21094, 049587, 1100.000000 5.00 >END OF FILE t, -cl 9.L ~ i::, /;B,':R ~-3 /1AC Jr, ^J 2 bfgf sq?. {; fi1~t~ FALE: 4 eCCEL 4I j t fr; RES I7R $StA3 &Sw | - T64,0 /S: ( 5. - /.,, r: \' pa-o ra, ay HEAvy Le y4 $Z 4# f=trL loO t C /m?HIST V=AA CASES=1-45 0P:HIST7 INTERVAL EXPRESSI0N -- #INT: (MINI MAX) ( MI N MAX)/WIDTH #PER/( MI N MAX) HIS TGRAM CASES - CASE#: 1-45 MIDPOINT HIST7 COUNT FOR 1.AA (EACH X= 1) 0. 20.0 9 + XXXVsXXX~X 676.67 46.7 21 + XXXXXXXXXXXXXXXXXXXX 1353.3 22.2 10 +XXXXXXXXXX 2030.0 8.9 4 +XXXX 2706.7 0. 0 + 3383.4 0. 0 + 4060.0 2.2 1 +X T0TAL 45 (INTERVAL WIDTH- 676.67) C0MMAND?HIST V=AA CASES-1-45 OP=HISTZ INTERVAL EXPRESSI0N -- #INT: (MIN. AX) (MIN,MAX)/WIDTH #PER / ( MI N, MAX) HIST0GRA M CASES CASE#: 1 -4 5 MIDPOINT HISTZ CCUNT F0R 1.AA (EACH X- 1) 0. 20.0 9 +XXXXXXXXX 676.67 46.7 21 +XXXXXXXXXXXXXXXXXXXXX 1353.3 22.2 10 -+XXXXXXXXX 2030.0 8.9 4 +XXXX 2706.7 0. 0 + 3383.4 0. 0 + 4060.0 2.2 1 +X T0TAL 45 (INTERVAL WIDTH- 676.67) C0 MMA N D?DESCRIBE V=AA CASES-1-45 DESCRIPTIVE (IEASURES CASES -CASE#: 1-45 \IaTArnl V!,J NM TMTIIMl MAXIMII ME 1AN STD DEV

I.AA 45 0. 4060.0 851.28 735.72 COMMAND?DIST V=AA CASES=1-45 PROB-.5 DISTRIBUTI0NAL ANALYSIS CASES=CASE#: 1-45 CUMULATIVE SAMPLE DISTRIBUTION OF I.AA N- 45 OUT OF 45 1.00000 + *.90000 + 3 * 2.80000 + 3.70000 + ** 3.60000 + 2 2.50000 + * 2.40000 + 3.30000 + 5.20000 + * 2.10000 + ** * O. + +- - - - -t - - - -t- _ _ _..... _ _+....+ _ _ _ _+ t _ L _ _ _+ t _ t _ _ ____+ - _-.. + _ _ _ 0. 1624.0 3248.0 AA 812.01 2436.0 4060.0 PROB QUANTILE.5000 632.73 CO MMA N D?REGRFSS V=AA;Q CASES=1-45 LEAST SQUARES REGRESSI0N CASES-CASE#:I-45 U. 305 '/AgO ANALYSIS 0F VARIANCE OF I.AA N: 45 0UT 0F 45 S0URCE DF SUI SQRS MEAN SQR F-STAT SIGNIF REGRESSI0N 1.25527 +6.25527 +6.46589.4985 ERR0R 43.23561 +8.54795 +6 TaTA1 A 9 q!1 t 4-Q

ttULT R-.10353 R-SQR=.01072 SE= 7o0.22 VARIABLE PARTIAL C0EFF STD ER RF( T-STAT SIGNIF CONSTANT 944.69 175.80 ' 5.3736.0000 4.Q -.1 0353 -5.9627 8.7357 rV -.68256.4985 CO MMA ND)? W _~~~~-.,. rc) / 0i\CD- '-. 10 Z 4,I o~~~~~y

?HIST V-AA CASES-46-129 OP-HIST% INTERVAL EXPRESSION -- #INT: (MIN MA) MIN, MAX)/WIDTH #PER / (MIN, MAX) HIST0GRAMi CASES-CASE#:46-129 5o MIDPOINT HIST% COUNT FOR I.AA (EACH X- 2) -7381.8 1.2 1 +X -4921.2 0O 0 + -2460.6 1.2 1 +X.62497 -1 3.6 3 +XX 2460.7 75.0 63 + XXXXXXXXX)x)(XXXXXXXXXXXxxxxxxx 4921.3 14.3 12 +XXXXXX 7381.9 1.2 1 +X 9842.5 2.4 2 +X 12303. 0. 0 + 14764. 1.2 1 +X TOTAL 84 (INTERVAL WJIDTH- 2460.6) COMMA ND?DESCRIBE V-AA CASES=46-129)*DESCRIPTIVE MEASURES CASES -CASE#: 4 6-12 9 VARIABLE N MINIMUM MAXI MUM MEAN STD DEV.AA 84 -7381.8 14764. 2879.7 2389.0 cOrCNKA NO?DIST V:AA CASES ---46-129 PROB-.5 DISTRIBUTIO0NAL ANALYSIS CASES:CASE#:46-129 CUMULATIVE SAMPLE DISTRIBUTION Or I.AA N- 84 OUT OF 84 1.00000 + 2 * 4*.90000 + 4.80000 + 5.70000 + 2

.60000 + 3 5.50000 + 6.40000 + 7.30000 + 3 4.20000 + 2 9.10000 + 0. +* + _...+.... _ _ _ ___+.+.. _ _+... _+.. _..+....+ _.. _ _._ _+ _ _ _.+ -7381.8 1476.4 10335. AA -2952.7 5905.5 1 4764. PROB QUANTILE.5000 2509o.8 SrrWLe EGR es&ON 5'wAr C0 MA ND?REGRESS V=AA;Q CASES46 —:46-129 LEAST SQUARES REGRESSI0N CASES:CASE#:461: 4 2- L- so -/ ANALYSIS BOF VARIANCE OF 1.AA N- 84 OUT 0F 84 S0URCE DF SUM SQRS MEAN SQR F-STAT SIGNIF REGRESSI0N 1.11675 +8.11675 +8 2*0719.1538 ERROR 82.46205 +9.56347 +7 T0TAL 83.47372 +9 MULT R. 15699 R- SQR-.024 64 SE- 2373.8 VARIABLE PARTIAL COEFF STD ERROR T-STAT SIGNIF C0NSTANT 3402.7 446.23 7.6255.00.00 4.Q -.1 5699 -29.388 20.417 -1.4394.1538~ ~~~~~~Y b -t-+~~~ m (7) C0MMAND ~ 4 _ 63oa_ ~~r&9,~~

?HIST V=AA CASES-130-185 OP-HIST% INTERVAL EXPRESSI0N -- #INT: (IIN, MAX) (MIN, MAX)/WIDTH #PER/(MIN, MAX) HIST0GRAM CASES-CASE#:130-185 MIDPOINT HIST% C0UNT F0R I.AA (EACH X- 1) 738.19 108 1 +X 2952.8 089 5 +XXXXX 5167.3 19.6 11 +XXXXXXXXXXX 7381.9 28.6 16 +XXXXXXXXXXXXXXXX 9596.5 23.2 13 + XXXXXXXXXXXXX 11811. 12.5 7 +XXXXXXX 14026. 3.6 2 +XX 16240. 1.8 I +X T0TAL 56 (INTERVAL WIDTH- 2214.6) C0MMAND?3ESV*-SCRIBE V-AA CASES-130-185 ERROR -- INVALID COMMAND: DESSCRIBE" COMMAND CANCELLED C0 MMA ND?DESCRIBE V:AA CASES-130-185 DESCRIPTIVE MEASURES CASES:CASE#: 130-1 85 %bS Wk"' "'filNTnM VAAEl ulh SI ` l 1.AA 56 738.19 16240. 7871.8 3195.2 C0MMAND?DIST V-AA CASES-130-185 PROB.5 DISTRIBUTI0NAL ANALYSIS CASES-C.SE#:130-185 CUMULATIVE SAMPLE DISTRIBUTI0N 07 1,AA N- 56 0UT OF 56 1.00000 + * *00 *.90000 + 3

.80000 +.70000 + 4*.60000 + 4 5.50000 + 2.40000 + 5.30000 + 4.20000 + ** 4.10000 + * *,2 O. + 738.19 6939.0 13140. AA 3838.6 1 0039. 1 6240. PROB QUANTILE.5000 7381.9 C 0 Ml A ND?REGRESS V:AA;Q CASES:130-185 LEAST SQUARES REGRESSI0N CASES:CASE#:130-185 -5 - eI5 _ ANALYSIS 0F VARIANCE OF 1.AA N- 56 OUT OF 56 SOURCE DF SU.M SQRS MEAN SQR F-STAT SIGNIF REGRESSION 1.12325 +9.12325 +9 1 5.1 85.0003 ERROR 54.43828 +9.81163 +7 TOTAL 55.56153 +9 MULT R-.46849 R-SQR-.21949 SE- 2848.9 VARIABLE PARTIAL COEFF STD ERROR T- ST AT SIGNIF C0ONSTANT 9991.2 663.89 1 5.050c.0000 4.Q -.46849 -1 04.57 26.835 -3.8968.0003 COMM.AND -r 9 q _o(6Cs9)? Ah' cS99

HIST V:AA CASES=186-246 1-OP-=HIST% INTERV@L EXPRESSION -- #INT:('lIIN, MAX) (MIN,MAX) /WIDTH #PER/( MIN, MAX) HISTOGRAM CASES:CASE#: 186-246 U - 754 MIDPOINT HIST% COUNT?rPR 1,AA (EACH X= 1) 2214.6 1.6 I +X 4640.0 26.2 16 + XXXXXXX;(XXXXXX 7065.5 31.1 19 +XXXXAXXXXXXXXXXXXXXX 9491.0 13.1 8 +XXXXXXXX 11916. 14*8 9 +XXXXAXXXX 14342, 8.2 5 +XXXXX 1 76767. 3,3 2 +XX 19193. 1.6 1 +X TOTAL 61 ( I NTERVAL WIDTH- 2425.5) COMMA ND?DESCRIBE V:186-246#?DESCRIBE V=AAB+- CASES=186-246 DESCRIPTIVE MEASURES CASES-CASE#:186-246 VARIABLE N MINIMUM MAXIMUM MEAN STD DEV i.AA 61 2214.6 19193. 8525.5 3661.7 COMMAND?OfS'r '/A4 CASES-=86-246 PR zB=.*5 DISTRIBUTIONAL ANALYSIS CASES = CASE#: 1 86-2 46 CUMULATIVE SAMPLE DISTRIBUTION OF 1.AA N= 61 OUT 0F 61 1.00000 + 2 * 3 *,90000 + 4 *.80000 + 4 *.70000 + 2 5

,~UUUU t -.50000 +.40000 + * 2 4.30000 + 2 6.20000 + 3.10000 + 2 3 0. 2214.6 9005.9 15797. AA 561 0.2 12402. 191 93. PROB QUANTILE.5000 8120.1 CO MMA N D ) Mo?REGRESS V-AA;Q CASES-186-246 75 ~ '~_ LEAST SQUARES REGRESSION CASES-=CA3SE#:186-246 ANALYSIS OF VARIANCE OF 1.AA N: 61 OUT OF 61 SOURCE DF SUM SQRS iYAN SQR F-STAT SIGNIF REGRESSION 1.26170 +9.26170 +9 28.446.00000 ERROR 59.54280 +9.92000 +7 TOTAL 60.80450 +9 MULT R:.57035 R-SQR-.32530 SE: 3033.1 VARIABLE PARTIAL COEFF STL) ERROR T-STAT SIGNIF CONSTANT 1352 6. 1 014.8 13.328.0000 4.Q -.57035 -265.25 49.733 5.3335.0000 COMMAND 44:; 35a2C~, 6 j)

HIST#?HIST V=AA CASES=247-327 0P-HIST% INTERVAL EXPRESSION -- #INT: (MIN,MAX) ( MI N, iAX) /WIDTH # PER/( MI N,MAX) HISTOGRAM CASES=CASE#:247-327 L _-' I/, MIDPOINT HIST7 COUNT FOR 1.AA (EACH X I ) 2952.8 1 2 1 +X 5085.3 12.3 10 +XXXXXXXXX 7217.8 22.2 18 + YXXXXXXXXXXXXXXX 9350.4 25.9 21 + X(XXXXX(XXXXXXXXXXXXXX 1 1 483. 1 9.8 1 6 +XXXXXXXXXXXXXX 13615. 2.5 2 +XX 15748. 9.9 8 + XXXXXXXX 17881. 3.7 3 +XXX 20013 1.2 1 +X 22146. 1.2 1 +X TOTAL 81 (INTERVAL WIDTH: 2132.5) COMMA ND?DESCRIBE V=AA CASES=247-327 DESCRIPTIVE MEASURES CASES -4ASE#:247-327 VARIABLE N MI N I iU iM IA XI MIJ1U MEA N STD DEV I.AA 81 2952.8 22146. 10201. 3819.4?REGRESS V=AA;Q CASES=247-2-327 >: 5 (tO 4 / LEAST SQUARES REGRESSION CASES:CASE#:247-3 7 ANALYSIS 07 VARIANCE OF 1.AA N= 81 OUT 0 81 SOURCE OF SUM SQRS Mi EAN SQR F-STAT SIGNIF REGIR"ESSION 1.45454 +7.45454 +7.30890.5799 ERROR 79.11625+10.14715 +8 TOTAL 80.11670+ 10 M ULT R:.06241 R-SQR -.00359 SE- 383,.0 VARIABLE PARTIAL COEFF ' STD,lRROR T-STAT SIGNIF CONSTANT 10512. 703.91 1 4.934.0000 4.Q -.06241 -17.273 31.079 -.55579.5799

C0MMAND?DIST V:AA CASES:247-327 P0-R0B=,.5 DISTRIBUTIONAL ANALYSIS CASES:CASE#:247-327 CUMULATIVE SAMPLE DISTRIBUTION 0F 1.AA N- 81 OUT OF 81 1.00000 + * * 3 5.90000 +.80000 + 5 4.70000 + 6 9*.60000 +.50000 + 5 52.40000 + 7.30000 +.20000 + 3* 2*.1 0000 +- 3* 0 + -I- _..._....++.... +.....F.... +.... --- _ _ - I-..!-....+ 2952.8 10630. 18307. AA 6791.3 14469. 22146. PROB QUANTILE.5000 9596.5 C0O MiMAND Rob 3/ t.*3 lx~uiit

REGRESS V-AA;Q CASES TO SELECT:A LL LEAST SQUARES REGRESSI0N ANALYSIS OF VARIANCE 0F 1.AA N: 327 OUT OF 327 S0URCE DF SUM SQRS MEAN SQR F-STAT SIGNIF REGRESSIO N 1.71320 +8.71320 +8 3.3347.0688 ERROR 325.69509+10.21 387 +8 TOTAL 32 6.70222+10 MULT R-.10078 R-SQR-.01016 SE: 4624.6 VARIABLE PARTIAL C0EFF STD ERROR T-STAT SIGNIF C0NSTANT 6998.8 450.21 15.546.0000 4.Q -.1 0078 -37.21 6 20.350 -1.8261.0688 C0OMMAND?TRANS TRANSF0RMtATI0N EXPRESSI0N (E.G., V'9=V2+V5 0R VI O=SQRT( V8) ):VI!O-L0GIO(AA) L=LA ERROR -- SYNTAX: VI O=LG1 O(AA) L=LA ENTER NEW VALUE FOR TRANSFORMATION EXPRESSI0N (E.G., V9=V2+V5 0R V1 O= SQRT(V8) ) ERROR -- ILLEGAL VALUE THE EXPRESSION STARTS WITH "VK=", WHERE 0 < K < 10000; -THE RIGHT-SIDE MAY BE. A, A OP B, FCN", FCN(A), FCN(A,B), WHERE A AND B ARE VARIABLES AND/0R C0NSTANTS WITH DECIMAL P0INTS, FCN IS FUNCTI0N NAME. ENTER NEW VALUE FOR TRANSFORMTATION EXPRESSI0N (E.G., V9=V2+V5 OR V1 O= SQRT(V8) ) =V20 L0G1 0 (AA) LABEL F0R THE RESULT VARIABLE(S) -LAA LOGI O TRANS F0RMATI 0 N VARIABLE T0TAL VALID lISS 20.LAA 327 323 4 C0 1MAN D?REGRESS V=LAA;Q CASESE,-ALL

LEAST SQUARES REGRESSI0N ANALYSIS POF VARIANCE 0F 20.LAA N: 323 OUT OF 327 SOURCE DF SUM SQRS MEAN SQR F-STAT SIGNIF R EGR ESSI0N 1.39460.39460 1.9284.1659 ERR0R 321 65.685.2 04 63 T0TAL 322 66. 080 MULT R-.07728 R-SQR-.00597 SE-.45236 VARIABLE PARTIAL COEFF STD ERROR T-STAT SIGNIF CO NSTA NT 3.694 6.44400 -1 83.211 0. 4.Q -.07728 -.27783 -2.20007 -2 -1.3887.1 659 C 0 MMA ND?DIST V=LAA CASES-ALL 0P-==-HIST% ERR0R -- INVALID KEYW0RD: 0P-HIST%Z DISTRIB'JTIONAL ANALYSIS CUMULATIVE SAMPLE DISTRIBUTION OF 20.LAA N- 323 OUT OF 327 1.00000 + 52* x.90! $.07 USED. CONTINUE(YES/NJ) Z70200 DATA CHECK.?7.0200 DATA CHECK.??7# RES Y OR N?N C0MMAND?HIST-V#?HIST V=LAA CASES=ALL OP=HIST% INTERVAL EXPRESSI0N -- #INT: (MIN, IAX) (MIN,MAX)/WIDTH #PER/(MIN,MAX) HIS TGRAM MIDP INT HISTZ COUNT 140OR 20.LAA (EACH X= 2) 1.8682.6 2 X 2.0139 0. 0 + 2.1596 0. 0 + 2.3055.6 2 +X 2.4510 1.2 4 +XX 2.5967 1.9 6 +XXX( 2.7424 3.1 10 +XXXXX 2.8882 1.5 5 +XXX 3.0339 2.5 8 +XXXX 3.1796 6.8 22 + XXXXXXXXXX 3.52 53 7.7 2 5 + XXXXXXXXXXXX /1 "7 n 7 7 9 ~ 4-c(X fXZ;~X X

3.,7 62/4 13.0 42 +XXXXXXXXXXXXXXXXXXXXX 3.9081 1 7.6 57 +XXXXXXXXXXXXXXXXXXXXXXXXXXXXX 4.0539 19.2 62 + XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 4.1996 5.9 19 +XXXXXXXXXX 4.3453.9 3 +XX MISSING 4 T0TAL 327 (INTERVAL WIDTH-.14571) C0MMA ND?R EA D N0TE. THIS DATASET CURRENTLY HAS 5 VARIABLES AND 327 CASES FILE C0NTAINING DATA OR * T0 ENTER DATA HERE -WG ABAR F0RMAT SPECIFICATION OR * T0 ENTER DATA SEPARATED BY COMMAS:: +-* VARIABLES TO READ (E.G., 1-10) -1 -4 LABELS CORRESPONDING TO THESE VARIABLES OR * FOR STANDARD LABELS:AAC, RC, U, Q CASES TO ASSIGN TO THE DATA BEING READ (E.G., 1-98) READ OBSERVATIONS 1-327 VARIABLES BY CASE 327 CASES READ FOR 4 VARIABLES CASES CHANGED FOR 4 EXISTING VARIABLES C0MMAND?REGRESS V=AAC;Q CASES=ALL LEAST SQUARES REGRESSI0N ANALYSIS OF VARIANCE 0F 1.AAC N- 327 OUT 0F 327 S0URCE DF SUM SQRS MEAN SQR F-STAT SIGNIF REGRESSI0N 1.662 58+11.662 58+11 3.3347.0688 ERROR 325.64576+1 3. 1 9869+1 1 T0TAL 326.65238+13 MULT R-.10078 R-SQR.01016 SE-.14096 +6 VARIABLE PARTIAL COEFF STD ERROR T- STAT SIGNIF C0 NSTANT.21332 +6 13722. 1 5.546.0000 4.Q -.1 0078 -1 134.4 621.19 -1.8261.0688 C0MM A N D? TR A NS TRANSF0RMATI0N EXPRESSI0N (E.G., V9-V2+V5 0R VI O:SQRT(V8) ):V30- L0G1 O (AAC) LAB EL FOR THE RESULT VARIABLE(S) -LAAC

L0GIO TRANSF0RMATI0N VARIABLE TOTAL VALID MISS 30.LAAC 327 323 4 COMMAND?REGRESS V:LAAC;Q CASES:ALL LEAST SQUARES REGRESSI0N ANALYSIS OF VARIANCE OF 30.LAAC N- 323 OUT 0F 327 S0 URCE DF SUM SQRS MEAN SQR F-STAT SIGNIF REGRESSION 1.39460.39460 1.9284.1659 ERROR 321 65.685.20463 TO TAL 322 66.080 MULT R-.07728 R-SQR-.00597 SE-.45236 VARIABLE PARTIAL COEFF STD ERROR T-S AT SIGNI F C0NSTANT 5.1786.44400 -1 116.64 0. 4.Q -.0772 8 -.27783 -2.20007 -2 -1.3887.1659 C0 MMA ND?SIG NFF ERR0R -- INVALID COMMAND: SIGN0FF" C0 iMA ND CANCELLED CO MMA ND?STOP USE $RES TO RE-ENTER MIDAS #SIGNOFF #OLU 15:39:40-17:22:21 FRI MAR 31/78 #Tr ER M, NR MAL, UNI V hELAPSED TIME 102.685 MIN. $2.40 #CPU TIME USED 3.021 SEC. $.49 #CPU STOR VMI 4.116 PAGE-ifIN. $.24 #WAIT STOR VMI 141.476 PAGE-HR. #DR'JM READS 5806 #APPROX. COST OF THIS RUN IS $3.23 iDISK STORAGE 128 PAG E-HR. $. 01 #APPROX. REMAINING BALANCE. $73.29

.: ]i. * 3...,.......~.;.. -, -.* e:~ r, L,, I: I EL.._ * t Ja ~ ' c ' _.<; -.: -.i i i-. 0.. t i. r.. -- c~ IL ( (IAA~srAJr A "*..":,-. 8Y.E,4V... Y,'.:; ~ -,; jr: t.....;:..).P' 4 Z - * P" --- a.. a' V -;,;a ra~a-t~ -, / ~ -, L;a V(c 5i/V!.R*T1 - "- t, ~,. 4~ - *. a,,;t*, a, a. a, — 1. {3 E{Y rv s oo o i, r... *v i,. -..,..: ti L,* r 8~ (~'. /_. t,~,,T i., Ir -- -SP r ~etrY ) F t/ - ( c.. ~ ~ ~ ~ ~ __ } \,<. B3'V V LCS~ bq _oLW~~ F PLh er fhw, ~* i j:. - r J t;w*, _+, t VrI. s _ f rr AV~ C3?E t3_ Fcj$ ~ " *~~ _. _.L R S.E ~ 9T~~:?=~,~. _,., _..... 13 tT 1, *.._, f

SIGNON ODLU #ENTER USER PASSWORD.?STEAM #TERM, NORMAL, UNIV #**LAST SIGNON WAS: 00:19:25 TUE APR 04/78 # USER "ODLU" SIGNED ON AT 17:27:51 ON WED 'APR 05/78 #F AVGACCEL CUMACCEL LF LINEFIT MDPRDATA.- PFfLE PLOTI PLOT2 QACCEL- TDATA TEMP WATERDROP WD WHATA WDGRAF WG WGABAR WGAVG #LIST QACCEL. > 1 19192.91406 0.75F39 1100.00000 0.0 2 15501.96875 0.61254 I1100.00000 0.0 > 13 738 1.-89063 0.29169 1100.00000 0.0 > 4 2030.01978 2.24796 305.00000 5.0 > 5 1328. 74023 1.10043 305.00000 5.0 > 6 1722.44116 1.42GAB 305.00000 5.0 >ATTN! 4RUN STATs:.MIDAS EXECUTION BEGINS M I D A'S STATISTICAL RESEARCH LABORATORY UNIVERSITY OF MICHIGAN 17:30:46 APR 5, 1978 COMMAND?READ FILE CONTAININ- DATA OR TO ENTER DAPTA HEHE:*_QA CCEL FORWAT SZEtWIFIUTlON1 UR Ii T0 E NT YF D lI 5E6.tfT~ rY pf 7N ez:4(F15.5, IX) VARIABLES TO READ (E.G., 1-10):1-4 LABELS CORRESPONDING TO THESE VARIABLES OF * FOP STANDARD LAIELS:AA,R,U,Q CASES TO ASSIGN TO THE DATA BEING READ (E.G., 1-98):1-327 READ OBSERVATIONS 1-327 VARIABLES BY CASE 327 CASES READ FOR 4 VARIABLES C OMMA ND?WRrTTF V-ALL CASES=!

-ILE TO RECEIVE DATA OR * TO WRITE DATA.HERE ORMAT SPECIFICATION OR * TO LIST DATA WITH HEADINGS 4RITE OBSERVATIONS CASES-CASE# *I-6 JARIABLES BY CASE 1. 2. 3. 4. R U Q 19193..75839 1100.0 0. 15502..61254 1100.0 0.' 7381.9.29169 1100.0 0. 2030.0 2.2480 305.00 5.0000 1328.7 1.1004 305.00 5 0000 1722.4 1.4265 305.00 5.0000; CASES WRITTEN FOR 4 VARIABLES 'OMMAND )ESCRIBE V:AA CASES=ALL )ESCRIPTIVE MEASURES VARIABLE N MINIMUM MAXIMUM MEAN STD DEV I.AA 327 — 7381.8 22146. 6322.2 4641.2 OM MA ND )IST V-AA CASES-ALL PROB=NOGRAPH:.25,.5,.75 )I STRIBUTIONAL ANALYSIS 'UMULATIVE DISTRIBUTION OF I.AA N- 327 OUT OF 327 PROB QUANTILE.2500 2399.1.5000 5659.4.7500 9596.5 ~OMMA ND

HIST V-AA CASES=ALL OP-HISTZ INTERVAL EXPRESSION -- #INT:(MIN,MAX) (MIN,MAX)/WIDTH #PEP/(MIN,MAX) HISTOGRAM MIDPOINT HIST%- COUNT FOR 1,AA (EACH X= 2) -7381.8.3 1 +X -574 1.4 0. 0 + -4101.0 0. 0 + -2460.6.3 1 +X -820.14.6 2 +X 820.28 15.9 52 +XXXXXXXXXXXXXXXXXXXXXXXXXX 2460.7 16,2 53 +XXXXXXXXXXXXXXXXXXXXXXXXXXX 4101.1 10.7 35 +XXXXXXXXXXXXXXXXXX 5741.5 9.5 -31 +XXXXXXXXXXXXXXXX 7381,9 15,0 49 +XXXXXXXXXXXXXXXXXXXXXXXXX 9022.4 9.5 31 +XXXXXXXXXXXXXXXX 10663. 7.6 25 +XXXXXXXXXXXXX 12303. 6. 1 20 +XXXXXXXXXX 13944. 2.8 9 +XXXXX 15584. 3 I1 10 +XXXXX 17224* 1.5 5 +XXX 18865..6 2 +X 20505. 0 0 + 22146..3 1 +X TOTAL 327 (INTERVAL WIDTH: 1640.4) COMMA ND?REGRESS V=AA;U CASES-ALL OPTION=MEANZERO LEAST SQUARES REGRESSION ANALYSIS OF VARIANCE OF 1.AA N: 327 OUT OF 327 SOURCE DF SUM SoRS MEAN SQR F-STAT SIGNIF REGRESSION I.16705+11.16705+11 1 607. 8 0. ERROR- 326.33871+10.10390 +g TOTAL 327.20092+11 OPT: MEANZERO R-SQR-.57491 SE- 3223.4 -VARIABLE PARTIAL COEFF STD ERROR T-STAT SIGNIF 3.U.91182 8.6755.21636 40.098 0. OMMAND

ZEGRESS V:AA;U CASES:ALL -EAST SQUARES REGRESSION kNALYSIS OF VARIANCE OF I.AA N= 327 OUT OF 32.7 SOURCE DF SUM SQRS MEAN SrR F-STAT SIGNIF REGRESSION 1.40371+10.40371+10 439.55.0000 ERROR 325.29851+10.91F48 +7 TOTAL 326,70222+10 MULT R=.75823 R-SQR=.57491 SE= 3030.6 VARIABLE PARTIAL COEFF STD ERROR T-STAT SIC'IF CONSTANT -3204.5 484.32 -6G.6G4.0000 3,U,75823 12.325.58787 20.965.0000 'OMMA ND

?SCATTER V-AA;U CASES ALL SCATTER PLOT N: 327 OUT OF 327 I.AA VS. 3.U AA 22146, + * + 2 2 3 16240. + * 5 * 3 2 * * + - 3 * 3 ~* 5 4 F X 10335. + 2 A 6 2 7 2 F X X + 7 3 7 c* 5 2 4 6 6 X 6 4429.2 +* 5 5 5 4 X 2 3 2 X 3 * * +X X X * * -1476.3 + + -7381.P + * 305.00 623.00 94!.00 U 464.00 782.00 1100.0 COMMAND

rRANS rRANSFORMATION EXPRESSION (E.G., V9=-V+V5 OR VI 0-SRT(V8) ) J20-SQRT(AA) LABELS=SRAA ERROR -- SYNTAX: "V20-SQRT(AA) LABELS=SRAA4 ~NTER NEW VALUE FOR TRANSFORMATION EXPRESSION (E.*.,!9-V2+V5 O0 I O=-SQRT(V8) ) J20=SQRT(AA).ABEL FOR THE RESULT VARIABLE(S) 3RAA SQRT TRANSFORMAT ION VARIABLE TOTAL VALID MISS 20.SRAA 327 324 3:OM MA ND URITE V-S ALL CASES-I-6 ILE TO RECEIVE DATA OR * TO WRITE DATA HERE FORMAT SPECIFICATION OR * TO LIST DATA WITH HEADIIGS dRITE OBSERVATIONS CASES-CASE-# 1-6 JARIABLES BY CASE 2. 3. 4. 20. tA R U Q SRAA 19193..75839 1100.0 0. 13F,54 15502..61254 1100.0 0. 124.51 7381.9.29169 1100.0 0. F5. V1 2030.0 2.2480 305.00 5.0000 45.05: 1328.7 1.1004 305.00 5.0000 36.452 1722.4 1.4265 305.00 5.0000 41.502; CASES WRITTEN FOR 5 VARIABLES 'OM MA ND )ESCRIBE V-SRAA CASES- ALL EAtSCRTI xtE tEASURES VARIABLE N rINIMUM tlAlItUM tiEA.,, STD DEV 20.SRAA 324 0. 148.81 73.991 30.692 OMMAND

HIST V=SRAA CASES-ALL OP-HIST. INTERVAL EXPRESSION -- #INT:(MIN,MAX) (MIN,MAX)/W!DTH #PER/(MtI,MAX) HISTOGRAM MIDPOINT HIST% COUNT FOR 20.SRAA (EACH X: 1) 0..3 1 +X 8.2675.6 2 +XX 16.535 3.4 11 +XXXXXXXXXX 24.802 4.9 16 +XXXXXXXXXXXXXXX 33.070 3.4 11 +XXXXXXXXXXX 41.337 7.7 25 +XXXXXXXXXXXXXXXXXXXXXXXXX 49.605 9.0 29 +XXXXXXXXXXXXXXXXXXXXXXXXXXXXX 57.872 7.7 25 +XXXXXXXXXXXXXXxXXXXXXXXXX 66.140 6.5 21 +XXXXXXXXXXXXXXXXXXXXX 74.407 9.3 30 +XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 82.675 8.3 27 +XXXXXXXXXXXXXXXXXXXXXXXXXXX 90 942 12.0 39 +XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXvXX 99.209 8.6 28 +XXXXXXXXXXXXXXXXXXXXXXXXXXXX 107.48 7.1 23 +XXXXXXXXXXXXXXXXXXXXXXX 115.74 5.2 17 +XXXXXXXXXXXXXXXXX 124.01 3.4 11 +XXXXXXXXXXX 132.28 1.5 5 +XXXXX 140.55.6 2 +XX 148.81.3 1 +X MISSING 3 TOTAL 327 (INTERVAL WIDTH- F.2675) COMMAND?DIST V-R_SRAA CASES: ALL PROB- NOGRAPH;.25,. 5,.75 DISTRIBUTIONAL ANALYSIS CUMULATIVE DISTRIBUTION OF 20.SRAA N- 324 OUT OF 327 PROB QUANTILE.2500 49.605.5000 76,847.7500 97.962 COMMAND

REGRESS V=SRAA;U CASES ALL OP-MEA.JZERO LEAST SQUARES REGRESSION ANALYSIS OF VARIANCE OF 20.SRAA N- 324 OUT OF 327 SOURCE DF SUM SQRS MEAN SQR F-STAT S GN IF REGRESSION I.19801 +7.19P01 +7 6527.6 0. ERROR 323 97979. 303.34 TOTAL 324.20781 +7 OPT: MEANZERO R-SQR=.68150 SE= 17.417 VARIABLE PARTIAL COEFF STD ERROR T-STAT SIGNIF 3.U.97614.94625 -1.11712 -2 P0.794 0. COMMAND

?SCATTER V=SRAA;U SCATTER PLOT N= 324 OUT OF 327 20.SRAA VS. 3.U;RAA 148.81 + * 2 g * 3 119.05 + 2 * * 4 4 C 3 4 4 + * 4 7 4 X 2 5 7 89.289 + 4 X 7 7 * 7 * 5 2 4 + 2 5 6 3 5 2 9 4 * 5 4 2 3 59.526 + 9 2 3 X 2 X * +3 X 4 X 7 2 29.763 +* * X * +S 2 O. +* + + + + +_ _ + _ _..+ _ + _ _ _ ++.. +.. + 305.00 623.00 041.00 U 464.00 782.00 1 100.0 COMMAND

lIST V:R_SRAA CASES 1-3 I-* {I STOGRAM CASES- CASE#: 1-3,IDPOINT COUNT FOR 20.SRAA (EACH X- 1) 85.918 1 +X 138,54 2 +XX TOTAL 3 (INTERVAL WIDTH: 52.621):OMMA ND )IST V-SRAA CASES-1-3 PROB-NOGRAPH;.25,.5,.75 )ISTRIBUTIONAL ANALYSIS CASES-CASE#- 1-3 UMULATIVE DISTRIBUTION OF 20.SRAA N: 3 OUT OF 3 PROB QUANTILE.2500 85.918.5000 124.5 1.7500 138.54 OMMAND ESCRIBE V-SRAA CASES= 13 ESCRIPTIVE MEASURES CASES=CASE# 1-3 VARIABLE N MINIMUM MAXIMUM MEAN STD DEV 20.SRAA 3 85.918 138.54 1 16.32 27.249 OMMAND

REGRESS V=SRAA;U CASES-1-3 OP=MEANZERO 9 _ 0 / LEAST SQUARES REGRESSION CASES-CASE#-1-3 ANALYSIS OF VARIANCE OF 20.SRAA N: 3 OUT OF 3 SOURCE DF SUM SORS MEAN SIR F-STAT STVNIF REGRESSION 1 40592. 40592. 54.670.0 17! ERROR 2 1485.0 742.49 TOTAL 3 42077. OPT: MEANZERO R-SQR-.00000 SE: 27.249 VARIABLE PARTIAL COEFF STD ERROR T-STAT SIG.N IF 3.U.98220.10575.14302 -1 7.3D39.0173 COMMA ND?SCATTER V=SRAA;U CASES-1-3 SCATTER PLOT CASES-CASE#*1-3 INVALID INTERVAL FOR 3.U: 1100.0, 1100.0 N O0 OUT OF 3 20.SRAA VS. 3.U COMMA ND

SCATTER V=SRAA;U CASES-4-58 SCATTE.R PLOT CASES-CASE#:4-58 N: 54 OUT OF 55 20.SRAA VS. 3.U 3RAA 130.30 + * + * 104.24 + *, 2 2. 2 + 3 II 2 78.181 + * 2 + 2 k 3 52.120 + 2 2 * 4 26.060 +4 2 0. +* +......+......+....+.....+....+....+. 305.00 623.00 94 1.00 U 464.00 782.00 1100.0 COMMA ND

HIST V-SRAA CASES:4-58 OP-HIST% I-* HISTOGRAM CASES-CASE#:4-58 MIDPOINT HIST% COUNT FOR 20.SRAA (EACH X- 1) 0. 1.9 1 +X 18.614 14 8 F s +XXXXXXXX 37.229 18.5 10 +XXXXXXXXXX 55.843 14.F 8 +XXXXXXXX 74.458 I1.1 6 +XXXXXX 93.072 25.9 14 +XXXXXXXXXXXXXX 111.69 7.4 4 +XXXX 130.30 5.6 3 +XXX MISSING 1 TOTAL 55 (INTERVAL WIDTH- 13.614) COMMAND?DIST V=SRAA CASES-4-58 PROB-NOGRAPH;.25,.5,.75 DISTRIBUTIONAL ANALYSIS CASES-CASE#-:4-58 CUMULATIVE DISTRIBUTION OF 20.SRAA N- 5'4 OUT OF 55 PROB QUANTILE.2500 36.452.5000 64.677.7500 94.118 COMMAND

DESCRIBE V-SRAA __=SRAAA_ CASES=4-58 DESCRIPTIVE MEASURES CASES=CASE#:4-5F VARIABLE N MINIMUM MAXIMUM MEAN STD DEW 20.SRAA 54 0. 130.30 65.P50 33.073 COMMA ND REGRESS V-SRAA;U CASES AL 4-58 OP MEANZERO q LEAST SQUARES REGRESSION CASES=CASE*:4-58 ANALYSIS OF VARIANCE OF 20.SRAA N- 54 OUT OF 55 SOURCE DF SUM SQRS MEAN SQR F-STAT SISNIF REGRESSION 1.27783 +6.27783 +6 1029.F.0000 ERROR 53 14299. 26 9 79. TOTAL 54.29213 +6 ~ OPT: MEANZERO R-SQR-.76080 SE: 16.425- r VARIABLE PARTIAL COEFF STD ERROR T-STAT SIGNIF 3.U.97522.95737 -1.29F34 -2 32.090.0000 COMMA ND

SCATTER V:SRAA;U CASES-59-130 --- 9 -,o (. SCATTER PLOT CASES-CASEsS59-130 N= 72 OUT OF 72 20.SRAA VS. 3.U SRAA 124.51 + * (R/cct) * 3 +............. 2 101.32 + 3 ad* / 2 + /3 3 /,. 2 2 78.141 + 2 * + * - 2 54.958 + 3/ 5 31.775 + +3 3 8.5918 +*. 305.00 623.00 041.00 U 464,00 782.00 1100.0 MO MM rdA ND?DESCRIBE V=SRAA CASES=59-130 DESCRIPTIVE MEASURES CASES-CASE#:59-130 VARIABLE N MINIMUM MAXIMUM MEAN STD DEV 20.SRAA 72 8.5918 124.51 77.39g 30.~37 COPiMA ND

HIST V=SRAA CASES=59-130 OP=HIST% I=* HISTOGRAM CASES=CASE#:59-130 MIDPOINT HIST% COUNT FOR 20.SRAA (EACH X: 1) 8.5918 2.8 2 +XX 23.08 6.9 5 +XXxx~ 37.571 4.2 3 +XXX 52.060 l1.1 13 +XXXXXXXXXXXXX 66.549 6.9 5 +XXXXX 81.039 12.5 9 +XXXXXXXXX 95.528 23.6 17 +XXXXXXXXXXXXXXXXX 110.02 22.2 16 +XXXXXXXXXXXXXXXX 124.51 2.8 2 +XX TOTAL 72 (INTERVAL WIDTH= 14.489) COMMAND DIST V:SRAA CASES:59-130 PROB:NOGRAPH;.25,.5,.75 UITRI!BUTIQN/L ANALYSIS CASES:CPSE:59-130 CUMULATIVE DISTRIBUTION OF 20.SRAA N= 72 OUT OF 72 PROB QUANTILE.2500 52.026.5000 85.*918.7500 101.66 O MMMA ND

REGRESS V=SRAA;U CASES:59-130 OP-MEANZERO a LEAST SQUARES REGRESSION CASES=CASE#:59-130 \NALYSIS OF VARIANCE OF 20.SRAA N- 72 OUT OF 72 SOURCE DF SUM SQRS MEAN SOR F-STAT SIGNIF REGRESSION I.4F093 +6.4%093 4+ 2007.4.0000 ERROR 71 17010. 239.5 TOTAL 72.49794 +6 OPT: MEANZERO R-SQR=.75104 SE: 15.478 VARIABLE PARTIAL COEFF STD ERROR T-STAT SI3NIF 3.U.98277.10040.22408 -2 44.F04.0000 COMMA ND

SCATTER V=SSR__S_RAA;U CASES-131-198 C iD SCATTER PLOT CASES=CASE: 131-1 9 N: 66 OUT OF 68 20.SRAA VS. 3. U 3RAA 138.54 + 2 +* 118.19 + i * 3 2 * 97.838 + * * 3 * 2 * * 77.488 +4 +* * 36.788 +4 +_ _.. _ + _ _+ +_ _ _ _ +_ _. _ +.+....+.. +...+..._+ 520.00 752.00 8F4.00 U 636.00 P68.CO 1100.O COMMAND DESCRIBE V=SRAA CASES-131-198 DESCRIPTIVE MEASURES CASES-CASE: 131-19F VARIABLE N MINIMUM MAXIrMU M MEAN STD DE'r 20.SRAA 66 36.788 138.54 F4.547 27.825 COMMA ND

RE#?HIST V:SRAA CASES-131-198 OP:HIST% I-* - <5 HISTOGRAM CASES CASE#: 13 1-19 MIDPOINT HIST% COUNT FOR 20.SRAA (EtCH X 1 ) 36.788 10.6 7 +XXXXXXX 49.507 10.6 7 +XXXXXXX 62.226 13.6 9 +XXXXXXXXX 74.944 6.1 4 +XXXX 87.663 12.1 F +XXXXXXXX 100.38 22.7 15 +XXXXXXXXXXXXXXX 113.10 15.2 10 +XXXXXXXXXX 125.82 7.6 5 +XXXXX 138.54 1.5 1 +X MISSING 2 TOTAL 68 (INTERVAL WIDTH- 12.719) COMMAND?DIST V-SRAA CASES=131-198 PROB-NOGRAPH;.25,.5,.75 DISTRIBUTIONAL ANALYSIS CASES-CASE#:131-198 CUMULATIVE DISTRIBUTION OF 20.SRAA N- 66 OUT OF 68 PROB QUANTILE.2500 66.552.5000 85.918.7500 105.23 COMMA ND?REGRESS V=SRAA;U CASES- 131-198 OP-MENZERO LEAST SQUARES REGRESSION CASES=CASE#: 13 1 - / 9- eS, ANALYSIS OF VARIANCE OF 20.SRAA N: 66 OUT OF 68 SOURCE DF SUM SQRS MEAN SqR F-STAT S I NIF REGRESSION 1.50215 +6.50215 +6 1635.1.0000 ERROR 65 19962. 307.10 TOTAL 66.52211 +6 OPT: MEANZERO R-SQR=.60911 SE- 17.524 VARIABLE PARTIAL COEFF STD ERROR T-STAT SIGNIF 3. U.98070.10115.25016 -2 40.437.0000 COMMAND

SCATTER V=SRAA CASES-199-250?,C ERROR -- WRONG # OF VARS: "SRAA ENTER NEW VALUE FOR VARIABLES -- VERTICAL; HORIZONTAL SRAA;U SCATTER PLOT CASES-CASE#: 199-250 N= 52 OUT OF 52 20*SRAA VS. 3.U SRAA 130.30 + 2 2 + * 2.* 86.599 + + * * * ~~~~~+ *2 2~~~~2 *2 2 642.797 + +2 2 ~4~~~ 42464.00897 72.00 I * * 21,046 +2 305.00 623.00 94 1.00 U 464.00 782.00 1100.0 COMMAND DESCRIBE V:SRAA CASES-199-250 DESCRIPTIVE MEASURES CASES-CASE#:199-250 VARIABLE N MINIMUM. MAXIMUM MEAN STD DEV 20.SRAA 52 21.046 130.30 71.219 31.705 COMMA ND

?HIST V-SRAA CASES-199-250 OP-HIST% I-* HISTOGRAM CASES CASE#: 199-250 MIDPOINT HIST% COUNT FOR 20.SRAA (EACH X- 1) 21.046 13.5 7 +XXXXXXX 36.653 9.6 5 +XXXXX 52.261 15.4 F +XXXXXXXX 67.869 13.5 7 +XXXXXXX p3.477 17.3 9 +XXXXXXXXX 99.085 17.3 9 +XXXXXXXXX 114.69 58s 3 +XXX 130.30 7.7 4 +XXXX TOTAL 52 (INTERVAL WIDTH: 15,60O) COMMA ND?DIST V=SRAA CASES=199-250 PROB=NOGRAPH;.25,.5,.75 DISTRIBUTIONAL ANALYSIS CASES-CASE#:199-250 CUMULATIVE DISTRIBUTION OF 20.SRAA N- 52 OUT OF 52 PROB QUANTILE *2500 47.059.5000 71.884.7500 94.11 I COMMA ND

REGRESS V=SRAA;U CASES-199-250 OP:MEANZERO LEAST SQUARES REGRESSION CASES CASE:* 19-250 ANALYSIS OF VARIANCE OF 20.SRAA N- 52 OUT OF 52 SOURCE DF SUM SQRS MEAN SQR F-STAT SISNI? REGRESSION i.30189 +6.301s9 +6 1173.1.0000 ERROR 51 13124. 257.34 TOTAL 52.31502 +6 OPT: MEANZERO R-SQR:.74400 SE- 16.042 VARIABLE PARTIAL COEFF STD ERROR T-STAT SIE IF 3.U.97895.91948 -1.26845 -2 34.251.0000 COMMA ND

?SCATTER V:SRAA CAS _ U CASES-251-294 Qy- 3-: SCATTER PLOT CASES-CASE#:251-294 N: 44 OUT OF 44 20.SRAA VS. 3. U ';RAA 127.44 + * 107.38 + 47.* 3 87.330 + 3 + * * * * 6 2. 67.277 + * 47.223 + +2 27.170 + * +_..+_....+ _ _ _ +_ _ _ _ +........+....+ _ _ _...+_.. +...+ _ _._.+ 520.00 752.00 8F4.OO U 635.00 F6g800 110. COMMA ND?DESCRIBE- V-SRAA CASES=251-294 DESCRIPTIVE MEASURES CASES=CASE#:25 1-294 VARIABLE N MINIMUM MUM MAXIMUM MEAI STD DEV 20.SRAA 44 27.170 127.44 73.952 c,1.!%6 COMMA ND 7

HIST V-SRAA CASES-251-294 OP-HIST% I-* HISTOGRAM CA SES CASE#:25 1-294 1I IDPOINT HIST% COUNT FOR 20.SRAA (EACH X- 1) 27.170 4.5 2 +XX 43.881 11.4 5 +XXXXX 60.592 13.6 6 +XXXXXX 77.303 38.6 17 +XXXXXXXXXXXXXXXXX 94.014 25*0 11 +XXXXXXXXXXX 110.73 4.5 2 +XX 127.44 2.3 1 +X TOTAL 44 (INTERVAL WIDTH: 16.711) COMMAND DIST V-SRAA CASES-* PROB=NOGRAPH;:_* ERROR -- INVALID CONSTANT: NOGRAPH:;* ENTER NEW VALUE FOR PROBABILITY POINTS NOGRAPH;.5,,25, 75 DISTRIBUTIONAL ANALYSIS CASES-CASE#:25 1-294 CUMULATIVE DISTRIBUTION OF 20.SRAA N- 44 OUT OF 44 PROB QUANTILE.5000 71.884.2500 60.753.7500 88.040 COMMA ND

?REGRESS V=SRAA;U CASES-251-294 OP:MEANZERO LEAST SQUARES REGRPESSION CASES:CASE#:251-294 'ANALYSIS OF VARIANCE OF 20,SRtA N- 44 OUT OF 44 SOURCE DF SUM SQRS MEAN SnR F-STAT SIGNIF REGRESSION I.?2416 +6.24816 +G q0o.49.0000 ERROR 43 11733. 272.96 TOTAL 44.259F9 +6 OPT: MEANZERO R-SQR:.42784 SE: 16.51F VARIABLE PARTIAL COEFF STD ERROR T-STAT SIGN IF 3.U.97717.83657 -1.27740 -2 30.15.00OCC COMMAND

SCATTER V-SRAA CASES=295-302 ERROR -- WRONG # OF VARS: "SRA A ENTER NEW VALUE FOR VARIABLES -- VERTICAL; HORIZONTAL SRAA, _;U SCATTER PLOT CASES-CASE#:295-302 INVALID INTERVAL FOR 3.U: 305.00, 305.00 N- 0 OUT OF g 20.SRAA VS. 3.U COMMA ND DESCRIBE V=SRAA CASES-* DESCRIPTIVE MEASURES CASES=CASE#:295-302 VARIABLE N MINIMUM MAXIMUM MEAN STD DEV 20.SRAA 8 9.0565 42.959 24.?30 11.166 COMMA ND DIST V-SRAA CASES-* PROB-NOGRAPH;.25,.5,.75 DISTRIBUTIONAL ANALYSIS CASES-CASE-'295-302;UMULATIVE DISTRIBUTION OF 20,SRAP. N- F OUT OF F PROB QUANTILE.2500 16.384.5000 22.194.7500 25.6t1 COMMA ND

?HIST V-SRAA CASES-* OP-* 1-* HISTOGRAM CASES-CASE#:295-302 I IDPOINT COUNT FOR 20.SRAA (EACH X- 1) 9.0565 2 +XX 25,008 4 +XXXX 42.959 2 +XX TOTAL 8 (INTERVAL WIDTH- 16.951) COMMAND q?REGRESS V-SRAA;U CASES=* OP:MEANZERO LEAST SQUARES RESRESSION CASES-CASE#:295-302 ANALYSIS OF VARIANCE OF 20.SRAA N- 8 OUT OF R SOURCE DF SUM SQRS MEAN SQR F-ST4T SI(NIF REGRESSION 1 4932.1 4932.1 39.557.0004 ERROR 7 872.77 124.68 TOTAL 8 5804.8 OPT: MEANZERO R-SQR-.00000 SE- I1.166 VARIABLE PARTIAL COEFF STD ERROR T-STAT SI NIF 3.U.92176.31409 -I.12944 -1 6.2895.0004 COMMA ND 7

3CATTER V:SRAA CASES-303-327 ' ERROR -- WRONG # OF VARS: * SRAA* ENTER NEW VALUE FOR VARIABLES -- VERTICAL; HORIZONTAL 3RAA;U 3CATTER PLOT CASES- CSE#:303-327 N= 25 OUT OF 25 20.SRAA VS. 3.U 3RAA 148.R1 + 126.07 + 103.32 + * + 80.571 + * * + * 57J.24 +* * 2 2 * 2 35.076 +* 520.00 752.00 1q4.OO U 636.00 868.00 1100.0:OMMA ND )ESCRIBE V=SRAA CASES-* )ESCRIPTIVE MEASURES CASES-CASE:303-327 VARIABLE N MIINIMUM MAXI MUM MEAN STD DEV 20.SRAA 25 35.076 148.81 70*386 28.315 O0 MMA ND

DIHIST V-SRAA CASES:* OP-HISTI-___ I-* HISTOGRAM CASES-CASE#:3030327 MIDPOINT HIST% COUNT FOR 20.SRAA (EACH X- 1) 35.076 16.0 4 +XXXX 57.824 44.0 11 +XXXXXXXXXXX 80.571 20.0 5 +XXXXX 103.32 12.0 3 +XXX 126.07 4.0 1 +X 148.81 4.0 1 +X TOTAL 25 (INTERVAL WIDTH- 22.748) COMMA ND?DIST V-SRAA CASES=* PROB-NOGRAPH;.25,.5,.75 DISTRIBUTIONAL ANALYSIS CASES-CASE#:303-327 CUMULATIVE DISTRIBUTION OF 20.SRAA N- 25 OUT OF 25 PROB QUANTILE.2500 48.991.5 000 60.753.7500 F3.742 COMMAND

REGRESS V=SRAA;U CASES=* OP=MEANZERO LEAST SQUARES REGRESSION CA SES-CASE#:303-327 %NALYSIS OF VARIANCE OF 20.SRAA N: 25 OUT OF 25 SOURCE DF SUM SQRS MEAN SQR F-STAT SIGNIF REGRESSION 1.13409 +6.13400 +6 357.18.0000 ERROR 24 9009.8 375.41 TOTAL 25.14310 +6 OPT: MEANZERO R-SQR=.53178 SE= 19.375 VARIABLE PARTIAL COEFF STD ERPOR T-STAT SIG NIF 3.U.96801.85139 -1.45049 -2 18.899.0000 COMMAND

UNIVERSITY OF MICHIGAN 3 901 5 03483 80551111111 3 9015 03483 8055