EXAMPLE 2. SIMPLE LINEAR REGRESSION: TV RATINGS DATA 1 14:45 Tuesday, August 14, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 36.11570 36.11570 18.38 0.0002 Error 28 55.02597 1.96521 Corrected Total 29 91.14167 Root MSE 1.40186 R-Square 0.3963 Dependent Mean 5.03333 Adj R-Sq 0.3747 Coeff Var 27.85154 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 1.70654 0.81715 2.09 0.0460 X 1 0.66536 0.15521 4.29 0.0002 EXAMPLE 2. SIMPLE LINEAR REGRESSION: TV RATINGS DATA 2 14:45 Tuesday, August 14, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Output Statistics Dep Var Predicted Std Error Obs Y Value Mean Predict 95% CL Mean 1 3.8000 3.3699 0.4648 2.4178 4.3221 2 4.1000 3.5030 0.4392 2.6032 4.4028 3 5.8000 3.6361 0.4144 2.7872 4.4850 4 4.8000 3.7692 0.3905 2.9693 4.5690 5 5.7000 3.9022 0.3676 3.1492 4.6552 6 4.4000 4.0353 0.3460 3.3266 4.7440 7 4.8000 4.1684 0.3259 3.5008 4.8360 8 3.6000 4.3014 0.3077 3.6712 4.9317 9 5.5000 4.4345 0.2916 3.8372 5.0318 10 4.1500 4.5676 0.2780 3.9980 5.1371 11 5.8000 4.7007 0.2674 4.1528 5.2485 12 3.8000 4.8337 0.2601 4.3008 5.3666 13 4.7500 4.9668 0.2564 4.4416 5.4920 14 3.9000 5.0999 0.2564 4.5746 5.6251 15 6.2000 5.2329 0.2601 4.7001 5.7658 16 4.3500 5.3660 0.2674 4.8182 5.9139 17 4.1500 5.4991 0.2780 4.9295 6.0686 18 4.8500 5.6322 0.2916 5.0349 6.2294 19 6.2000 5.7652 0.3077 5.1350 6.3954 20 3.8000 5.8983 0.3259 5.2307 6.5659 21 7.0000 6.0314 0.3460 5.3226 6.7401 22 5.4000 6.1644 0.3676 5.4115 6.9174 23 6.1000 6.2975 0.3905 5.4977 7.0974 24 6.5000 6.4306 0.4144 5.5817 7.2795 25 6.1000 6.5637 0.4392 5.6639 7.4634 26 4.7500 6.6967 0.4648 5.7446 7.6489 27 1.0000 3.3699 0.4648 2.4178 4.3221 28 1.2000 3.5030 0.4392 2.6032 4.4028 29 9.5000 6.5637 0.4392 5.6639 7.4634 30 9.0000 6.6967 0.4648 5.7446 7.6489 Output Statistics Std Error Student Obs 95% CL Predict Residual Residual Residual 1 0.3446 6.3953 0.4301 1.323 0.325 2 0.4938 6.5123 0.5970 1.331 0.448 3 0.6417 6.6305 2.1639 1.339 1.616 4 0.7883 6.7500 1.0308 1.346 0.766 5 0.9336 6.8709 1.7978 1.353 1.329 6 1.0775 6.9930 0.3647 1.358 0.268 EXAMPLE 2. SIMPLE LINEAR REGRESSION: TV RATINGS DATA 3 14:45 Tuesday, August 14, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Output Statistics Std Error Student Obs 95% CL Predict Residual Residual Residual 7 1.2202 7.1165 0.6316 1.363 0.463 8 1.3615 7.2414 -0.7014 1.368 -0.513 9 1.5015 7.3675 1.0655 1.371 0.777 10 1.6401 7.4951 -0.4176 1.374 -0.304 11 1.7773 7.6240 1.0993 1.376 0.799 12 1.9131 7.7543 -1.0337 1.378 -0.750 13 2.0476 7.8860 -0.2168 1.378 -0.157 14 2.1806 8.0191 -1.1999 1.378 -0.871 15 2.3123 8.1535 0.9671 1.378 0.702 16 2.4426 8.2894 -1.0160 1.376 -0.738 17 2.5716 8.4266 -1.3491 1.374 -0.982 18 2.6991 8.5652 -0.7822 1.371 -0.570 19 2.8253 8.7052 0.4348 1.368 0.318 20 2.9501 8.8465 -2.0983 1.363 -1.539 21 3.0736 8.9891 0.9686 1.358 0.713 22 3.1958 9.1331 -0.7644 1.353 -0.565 23 3.3166 9.2784 -0.1975 1.346 -0.147 24 3.4362 9.4250 0.0694 1.339 0.0518 25 3.5544 9.5729 -0.4637 1.331 -0.348 26 3.6714 9.7221 -1.9467 1.323 -1.472 27 0.3446 6.3953 -2.3699 1.323 -1.792 28 0.4938 6.5123 -2.3030 1.331 -1.730 29 3.5544 9.5729 2.9363 1.331 2.206 30 3.6714 9.7221 2.3033 1.323 1.742 Output Statistics Cook's Obs -2-1 0 1 2 D 1 | | | 0.007 2 | | | 0.011 3 | |*** | 0.125 4 | |* | 0.025 5 | |** | 0.065 6 | | | 0.002 7 | | | 0.006 8 | *| | 0.007 9 | |* | 0.014 10 | | | 0.002 11 | |* | 0.012 12 | *| | 0.010 EXAMPLE 2. SIMPLE LINEAR REGRESSION: TV RATINGS DATA 4 14:45 Tuesday, August 14, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Output Statistics Cook's Obs -2-1 0 1 2 D 13 | | | 0.000 14 | *| | 0.013 15 | |* | 0.009 16 | *| | 0.010 17 | *| | 0.020 18 | *| | 0.007 19 | | | 0.003 20 | ***| | 0.068 21 | |* | 0.016 22 | *| | 0.012 23 | | | 0.001 24 | | | 0.000 25 | | | 0.007 26 | **| | 0.134 27 | ***| | 0.198 28 | ***| | 0.163 29 | |**** | 0.265 30 | |*** | 0.187 Sum of Residuals 0 Sum of Squared Residuals 55.02597 Predicted Residual SS (PRESS) 65.50947 EXAMPLE 2. SIMPLE LINEAR REGRESSION: TV RATINGS DATA 5 14:45 Tuesday, August 14, 2001 The UNIVARIATE Procedure Variable: YRES (Residual) Moments N 30 Sum Weights 30 Mean 0 Sum Observations 0 Std Deviation 1.3774786 Variance 1.8974473 Skewness 0.13658782 Kurtosis -0.4752001 Uncorrected SS 55.0259716 Corrected SS 55.0259716 Coeff Variation . Std Error Mean 0.25149203 Basic Statistical Measures Location Variability Mean 0.00000 Std Deviation 1.37748 Median -0.06405 Variance 1.89745 Mode . Range 5.30628 Interquartile Range 1.98464 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 0 Pr > |t| 1.0000 Sign M 0 Pr >= |M| 1.0000 Signed Rank S -3.5 Pr >= |S| 0.9441 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.978618 Pr < W 0.7877 Kolmogorov-Smirnov D 0.079077 Pr > D >0.1500 Cramer-von Mises W-Sq 0.02521 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.186616 Pr > A-Sq >0.2500 Quantiles (Definition 5) Quantile Estimate 100% Max 2.9363406 99% 2.9363406 95% 2.3032688 90% 1.9808491 75% Q3 0.9686279 EXAMPLE 2. SIMPLE LINEAR REGRESSION: TV RATINGS DATA 6 14:45 Tuesday, August 14, 2001 The UNIVARIATE Procedure Variable: YRES (Residual) Quantiles (Definition 5) Quantile Estimate 50% Median -0.0640516 25% Q1 -1.0160129 10% -2.0225157 5% -2.3030073 1% -2.3699354 0% Min -2.3699354 Extreme Observations ------Lowest----- -----Highest----- Value Obs Value Obs -2.36994 27 1.09935 11 -2.30301 28 1.79778 5 -2.09830 20 2.16392 3 -1.94673 26 2.30327 30 -1.34908 17 2.93634 29 Frequency Counts Percents Percents Value Count Cell Cum Value Count Cell Cum -2.3699354417 1 3.3 3.3 0.0694124377 1 3.3 53.3 -2.3030072730 1 3.3 6.7 0.3647054017 1 3.3 56.7 -2.0983002370 1 3.3 10.0 0.4300645583 1 3.3 60.0 -1.9467312250 1 3.3 13.3 0.4347715943 1 3.3 63.3 -1.3490847430 1 3.3 16.7 0.5969927270 1 3.3 66.7 -1.1998692490 1 3.3 20.0 0.6316335703 1 3.3 70.0 -1.0337255863 1 3.3 23.3 0.9670589197 1 3.3 73.3 -1.0160129117 1 3.3 26.7 0.9686279317 1 3.3 76.7 -0.7821565743 1 3.3 30.0 1.0308490643 1 3.3 80.0 -0.7644438996 1 3.3 33.3 1.0654899077 1 3.3 83.3 -0.7014382610 1 3.3 36.7 1.0993462450 1 3.3 86.7 -0.4636593936 1 3.3 40.0 1.7977772330 1 3.3 90.0 -0.4175819237 1 3.3 43.3 2.1639208956 1 3.3 93.3 -0.2167974177 1 3.3 46.7 2.3032687750 1 3.3 96.7 -0.1975157310 1 3.3 50.0 2.9363406064 1 3.3 100.0 EXAMPLE 2. SIMPLE LINEAR REGRESSION: TV RATINGS DATA 7 14:45 Tuesday, August 14, 2001 The UNIVARIATE Procedure Variable: YRES (Residual) Stem Leaf # Boxplot 2 9 1 | 2 23 2 | 1 8 1 | 1 00011 5 +-----+ 0 66 2 | | 0 1444 4 | + | -0 422 3 *-----* -0 8875 4 | | -1 3200 4 +-----+ -1 9 1 | -2 431 3 | ----+----+----+----+ Normal Probability Plot 2.75+ +*+ | *+*++ | +*++ | *** | **** 0.25+ **** | **** | +*** | **** | ++*+ -2.25+ * ++*+* +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2