The SAS System 1 08:20 Thursday, September 11, 2003 Univariate Procedure Variable=Y Work Hours Moments N 25 Sum Wgts 25 Mean 312.28 Sum 7807 Std Dev 113.1376 Variance 12800.13 Skewness -0.07808 Kurtosis -0.63259 USS 2745173 CSS 307203 CV 36.22955 Std Mean 22.62753 T:Mean=0 13.80089 Pr>|T| 0.0001 Num ^= 0 25 Num > 0 25 M(Sign) 12.5 Pr>=|M| 0.0001 Sgn Rank 162.5 Pr>=|S| 0.0001 W:Normal 0.970756 PrF Model 1 252377.58081 252377.58081 105.876 0.0001 Error 23 54825.45919 2383.71562 C Total 24 307203.04000 Root MSE 48.82331 R-square 0.8215 Dep Mean 312.28000 Adj R-sq 0.8138 C.V. 15.63447 Parameter Estimates Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 62.365859 26.17743389 2.382 0.0259 X 1 3.570202 0.34697216 10.290 0.0001 Variable Variable DF Label INTERCEP 1 Intercept X 1 Lot Size The SAS System 5 08:20 Thursday, September 11, 2003 Plot of RESID*X. Legend: A = 1 obs, B = 2 obs, etc. | | 125 + | | | | A 100 + | | | A | 75 + | | | | A 50 + A A | A | A R | e | s 25 + A i | d | u | A a | A A l 0 + A | A A | A | |A A A -25 + | | A | | A -50 + A | A | A | A | -75 + | | A | | -100 + | -+------+------+------+------+------+------+------+------+------+------+- 20 30 40 50 60 70 80 90 100 110 120 Lot Size The SAS System 6 08:20 Thursday, September 11, 2003 Plot of RESID*PRED. Legend: A = 1 obs, B = 2 obs, etc. | | 125 + | | | | A 100 + | | | A | 75 + | | | | A 50 + A A | A | A R | e | s 25 + A i | d | u | A a | A A l 0 + A | A A | A | |A A A -25 + | | A | | A -50 + A | A | A | A | -75 + | | A | | -100 + | -+------+------+------+------+------+------+------+------+------+------+- 133.77 169.47 205.17 240.88 276.58 312.28 347.98 383.68 419.39 455.09 490.79 Predicted Value of Y The SAS System 7 08:20 Thursday, September 11, 2003 Plot of ST_RESID*X. Legend: A = 1 obs, B = 2 obs, etc. | | 2.5 + | | A | | 2.0 + | | A | | 1.5 + | S | t | A u | A d 1.0 + A e | A n | A t | i | A z 0.5 + e | d | | A R | A A e 0.0 + A s | A A i | A d | u | A A a -0.5 +A l | | A | | -1.0 + A | A A | | A | A -1.5 + | | | A | -2.0 + | -+------+------+------+------+------+------+------+------+------+------+- 20 30 40 50 60 70 80 90 100 110 120 Lot Size The SAS System 8 08:20 Thursday, September 11, 2003 Univariate Procedure Variable=RESID Residual Moments N 25 Sum Wgts 25 Mean 0 Sum 0 Std Dev 47.79534 Variance 2284.394 Skewness 0.316913 Kurtosis -0.39415 USS 54825.46 CSS 54825.46 CV . Std Mean 9.559067 T:Mean=0 0 Pr>|T| 1.0000 Num ^= 0 25 Num > 0 12 M(Sign) -0.5 Pr>=|M| 1.0000 Sgn Rank -7.5 Pr>=|S| 0.8448 W:Normal 0.978107 PrF Model 1 7896141.9614 7896141.9614 1.091 0.3070 Error 23 166395896.12 7234604.179 C Total 24 174292038.08 Root MSE 2689.72195 R-square 0.0453 Dep Mean 2193.01837 Adj R-sq 0.0038 C.V. 122.64931 Parameter Estimates Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 3590.908112 1442.1393863 2.490 0.0204 X 1 -19.969853 19.11502157 -1.045 0.3070 Variable Variable DF Label INTERCEP 1 Intercept X 1 Lot Size Sorted data by residual 13 08:20 Thursday, September 11, 2003 OBS X Y RESID RESIDSQ 1 50 157 -83.876 7035.18 2 100 353 -66.386 4407.11 3 70 252 -60.280 3633.68 4 60 224 -52.578 2764.44 5 30 121 -48.472 2349.53 6 40 160 -45.174 2040.68 7 110 421 -34.088 1162.00 8 20 113 -20.770 431.39 9 110 435 -20.088 403.53 10 50 221 -19.876 395.05 11 90 376 -7.684 59.04 12 90 377 -6.684 44.68 13 80 342 -5.982 35.78 14 100 420 0.614 0.38 15 80 352 4.018 16.14 16 90 389 5.316 28.26 17 70 323 10.720 114.92 18 50 268 27.124 735.71 19 40 244 38.826 1507.46 20 30 212 42.528 1808.64 21 70 361 48.720 2373.64 22 80 399 51.018 2602.83 23 120 546 55.210 3048.13 24 90 468 84.316 7109.18 25 30 273 103.528 10718.06 First step to find normal percentiles 14 08:20 Thursday, September 11, 2003 OBS X Y RESID RESIDSQ RANKRESI Z1 1 50 157 -83.876 7035.18 1 0.02475 2 100 353 -66.386 4407.11 2 0.06436 3 70 252 -60.280 3633.68 3 0.10396 4 60 224 -52.578 2764.44 4 0.14356 5 30 121 -48.472 2349.53 5 0.18317 6 40 160 -45.174 2040.68 6 0.22277 7 110 421 -34.088 1162.00 7 0.26238 8 20 113 -20.770 431.39 8 0.30198 9 110 435 -20.088 403.53 9 0.34158 10 50 221 -19.876 395.05 10 0.38119 11 90 376 -7.684 59.04 11 0.42079 12 90 377 -6.684 44.68 12 0.46040 13 80 342 -5.982 35.78 13 0.50000 14 100 420 0.614 0.38 14 0.53960 15 80 352 4.018 16.14 15 0.57921 16 90 389 5.316 28.26 16 0.61881 17 70 323 10.720 114.92 17 0.65842 18 50 268 27.124 735.71 18 0.69802 19 40 244 38.826 1507.46 19 0.73762 20 30 212 42.528 1808.64 20 0.77723 21 70 361 48.720 2373.64 21 0.81683 22 80 399 51.018 2602.83 22 0.85644 23 120 546 55.210 3048.13 23 0.89604 24 90 468 84.316 7109.18 24 0.93564 25 30 273 103.528 10718.06 25 0.97525 Using SAS to find normal percentiles 15 08:20 Thursday, September 11, 2003 OBS X Y RESID RESIDSQ RANKRESI Z1 NOR_PERC 1 50 157 -83.876 7035.18 1 0.02475 -1.96422 2 100 353 -66.386 4407.11 2 0.06436 -1.51920 3 70 252 -60.280 3633.68 3 0.10396 -1.25930 4 60 224 -52.578 2764.44 4 0.14356 -1.06444 5 30 121 -48.472 2349.53 5 0.18317 -0.90336 6 40 160 -45.174 2040.68 6 0.22277 -0.76286 7 110 421 -34.088 1162.00 7 0.26238 -0.63604 8 20 113 -20.770 431.39 8 0.30198 -0.51871 9 110 435 -20.088 403.53 9 0.34158 -0.40814 10 50 221 -19.876 395.05 10 0.38119 -0.30236 11 90 376 -7.684 59.04 11 0.42079 -0.19987 12 90 377 -6.684 44.68 12 0.46040 -0.09944 13 80 342 -5.982 35.78 13 0.50000 0.00000 14 100 420 0.614 0.38 14 0.53960 0.09944 15 80 352 4.018 16.14 15 0.57921 0.19987 16 90 389 5.316 28.26 16 0.61881 0.30236 17 70 323 10.720 114.92 17 0.65842 0.40814 18 50 268 27.124 735.71 18 0.69802 0.51871 19 40 244 38.826 1507.46 19 0.73762 0.63604 20 30 212 42.528 1808.64 20 0.77723 0.76286 21 70 361 48.720 2373.64 21 0.81683 0.90336 22 80 399 51.018 2602.83 22 0.85644 1.06444 23 120 546 55.210 3048.13 23 0.89604 1.25930 24 90 468 84.316 7109.18 24 0.93564 1.51920 25 30 273 103.528 10718.06 25 0.97525 1.96422 Normal probability plot 16 08:20 Thursday, September 11, 2003 Plot of RESID*NOR_PERC. Legend: A = 1 obs, B = 2 obs, etc. | | 125 + | | | | A 100 + | | | A | 75 + | | | | A 50 + A A | A | A R | e | s 25 + A i | d | u | A a | AA l 0 + A | AA | A | | AA A -25 + | | A | | A -50 + A | A | A | A | -75 + | | A | | -100 + | ---+-------------+-------------+-------------+-------------+-- -2 -1 0 1 2 RANK FOR VARIABLE RESID Correlation for correlation test for normality 17 08:20 Thursday, September 11, 2003 Correlation Analysis 2 'VAR' Variables: RESID NOR_PERC Simple Statistics Variable N Mean Std Dev Sum RESID 25 0 47.795336 0 NOR_PERC 25 0 0.968867 0 Simple Statistics Variable Minimum Maximum Label RESID -83.875960 103.528081 Residual NOR_PERC -1.964217 1.964217 RANK FOR VARIABLE RESID Pearson Correlation Coefficients / Prob > |R| under Ho: Rho=0 / N = 25 RESID NOR_PERC RESID 1.00000 0.99151 Residual 0.0 0.0001 NOR_PERC 0.99151 1.00000 RANK FOR VARIABLE RESID 0.0001 0.0