Class 27 Example: Height and Weight

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Class 27 Example: Height and Weight Case: Colonial Broadcasting (HBS: 9-894-011)

Heights and Weights of n=30 11-year-old girls CM Inches KG 135 53 26 146 57 33 153 60 55 154 61 50 139 32 131 52 25 149 59 44 137 54 31 143 56 36 35 141 28 136 151 48 155 133 34 164 65 47 37 46 147 58 152 140 42 148 29 30 144.800 57.067 36.167 Al used the regression of KG on CM to forecast the weight of a girl 144.8 cm tall. Al’s point forecast was _______________ Sample Means

Any three can be used to find the fourth. The regression line 𝑌 = 𝑎 + 𝑏 𝑋 𝑌 = 𝑎 + 𝑏 𝑋 Always goes thru 𝑋 , 𝑌 Any three can be used to find the fourth.

Heights and Weights of n=30 11-year-old girls CM Inches KG 135 53 26 146 57 33 153 60 55 154 61 50 139 32 131 52 25 149 59 44 137 54 31 143 56 36 35 141 28 136 151 48 155 133 34 164 65 47 37 46 147 58 152 140 42 148 29 30 144.800 57.067 36.167 Bo regressed KG on inches. Which model will be the better predictor of KG? Al’s Bo’s They should give identical results. Sample Means

Regression Statistics Multiple R 0.742 R Square 0.551 Adj R Square AL Regression Statistics Multiple R 0.742 R Square 0.551 Adj R Square 0.535 Standard Error 5.248 Observations 30 ANOVA df SS MS F Sig F Regression 1 946.892 34.376 0.000003 Residual 28 771.274 27.546 Total 29 1718.167 Coefficients t Stat P-value Intercept -71.371 18.366 -3.886 0.001 CM 0.743 0.127 5.863 BO Regression Statistics Multiple R 0.720 R Square 0.518 Adj R Square 0.501 Standard Error 5.439 Observations 30 ANOVA df SS MS F Sig F Regression 1 889.874 30.082 0.000007 Residual 28 828.293 29.582 Total 29 1718.167 Coefficients t Stat P-value Intercept -66.701 18.782 -3.551 0.001 Inches 1.803 0.329 5.485

Regression Statistics What if we use both?? SUMMARY OUTPUT Regression Statistics Multiple R 0.760 R Square 0.577 Adj R Square 0.546 Standard Error 5.187 Observations 30 ANOVA df SS MS F Sig F Regression 2 991.748 495.874 18.431 8.967E-06 Residual 27 726.419 26.904 Total 29 1718.167 Coefficients t Stat P-value Intercept -72.836 18.187 -4.005 0.0004 CM 2.180 1.121 1.946 0.0621 Inches -3.623 2.806 -1.291 0.2076

Which Girl was most over(under)weight?

How would you use these data to estimate the number of CM per inch?

Colonial Broadcasting Company Three Networks ABN, BBS, CBC Data from 88 made-for-TV movies (1992) CBC wants to know what factors affect the movie’s Rating. (the percent of US households with TVs tuned into a program) CBC needs to forecast the rating of a proposed movie.

. Obs Network Month Day Rating Fact Stars Prev Rating Competition 1 BBS 15.6 14.2 14.5 2 7 10.8 15.3 17.2 . 19 11 14.4 12.1 20 13.6 11.4 11.9 21 ABN 14.6 19.3 22 16.3 15.2 57 12 12.8 12.0 58 16.8 15.7 10.1 59 CBC 14.0 8.2 14.8 60 11.3 13.0 13.2 87 11.2 16.4 88 19.1 12.6 15.4 Average 5.88 4.25 13.82 0.41 13.77 14.06 Stdev 3.91 2.85 2.54 0.49 0.54 3.23 2.29 median 4 14.05 13.65 14.1 mode 13.8 min 8.9 5.3 max 19.5 24.7 20.3

1a. Rank the networks based on average 1992 rating. StatTools (Core Analysis Pack) Analysis: Regression 1. Dependent Variable: RATING Performed By: PEP Date: Thursday, May 04, 2006 Updating: Static Multiple R-Square Adjusted StErr of Summary R Estimate 0.3380 0.1143 0.0934 2.4212 Degrees of Sum of Mean of F-Ratio p-Value ANOVA Table Freedom Squares Explained 2 64.2912 32.14560148 5.4833 0.0058 Unexplained 85 498.3060 5.862423013 Coefficient Standard t-Value Lower Upper Regression Table Error Limit Constant 13.3633 0.4421 30.2299 < 0.0001 12.4844 14.2423 ABN 1.3972 0.5913 2.3627 0.0204 0.2214 2.5729 BBS -0.6483 0.6990 -0.9276 0.3563 -2.0380 0.7414 1b. How big was the ratings gap between the top and bottom ranked networks?

2a. What is the average rating of fact based movies? StatTools (Core Analysis Pack) Analysis: Regression 2. Dependent Variable: RATING Performed By: PEP Date: Thursday, May 04, 2006 Updating: Static Multiple R-Square Adjusted StErr of Summary R Estimate 0.2724 0.0742 0.0635 2.461 Degrees of Sum of Mean of F-Ratio p-Value ANOVA Table Freedom Squares Explained 1 41.7582 6.8950 0.0102 Unexplained 86 520.8390 6.0563 Coefficient Standard t-Value Lower Upper Regression Table Error Limit Constant 13.24615 0.34127 38.8141 < 0.0001 12.568 13.925 Fact 1.40107 0.53357 2.6258 0.340 2.462 2a. What is the average rating of fact based movies? 2b. Is the difference in fact and fiction ratings statistically significant?

fact-based movies had fewer stars (than fictional movies) StatTools (Core Analysis Pack) Analysis: Regression 3. Dependent Variable: RATING Performed By: PEP Date: Thursday, May 04, 2006 Updating: Static Multiple R-Square Adjusted StErr of Summary R Estimate 0.3733 0.1394 0.1191 2.387 Degrees of Sum of Mean of F-Ratio p-Value ANOVA Table Freedom Squares Explained 2 78.420 39.210 6.8836 0.0017 Unexplained 85 484.177 5.696 Coefficient Standard t-Value Lower Upper Regression Table Error Limit Constant 12.568 0.425 29.550 < 0.0001 11.72 13.41 Fact 1.799 0.541 3.327 0.0013 0.72 2.87 Stars 1.259 0.496 2.537 0.0130 0.27 2.24 3. Which is most true? fact-based movies had fewer stars (than fictional movies) Fact-based movies had more stars. Fact-based movies had the same number of stars. Cannont be determined.

StatTools (Core Analysis Pack) Analysis: Regression 5. Dependent Variable: RATING Performed By: PEP Date: Thursday, May 04, 2006 Updating: Static Multiple R-Square Adjusted StErr of Summary R Estimate 0.7387 0.5456 0.4799 1.834 Degrees of Sum of Mean of F-Ratio p-Value ANOVA Table Freedom Squares Explained 11 306.964 27.906 8.2964 < 0.0001 Unexplained 76 255.634 3.364 Coefficient Standard t-Value Lower Upper Regression Table Error Limit Constant 12.87691 2.01203 6.3999 8.870 16.884 Fact 1.89451 0.44028 4.3029 1.018 2.771 Stars 0.74425 0.42113 1.7673 0.0812 -0.095 1.583 Prev Rating 0.18571 0.10872 1.7081 0.0917 -0.031 0.402 Competition -0.29356 0.11035 -2.6602 0.0095 -0.513 -0.074 ABN 1.07497 1.03428 1.0393 0.3019 -0.985 3.135 BBS -1.04990 0.59970 -1.7507 0.0840 -2.244 0.145 OCT -1.54061 0.68598 -2.2458 0.0276 -2.907 -0.174 DEC 1.39816 0.72802 1.9205 0.0585 -0.052 2.848 APR-MAY -1.40377 0.56574 -2.4813 0.0153 -2.531 -0.277 MON 2.52860 1.00136 2.5252 0.0136 0.534 4.523 SUN 1.52567 0.70636 2.1599 0.0339 0.119 2.933 4. On Sunday night, CBC usually airs “Josette and Yvette” at 8 pm followed by the Sun night movie. “J&Y” typical get a 17.5 rating. If they replace “J&Y” with a rock concert expected to get a rating of 20, what is the expected change in the movie rating?

StatTools (Core Analysis Pack) Analysis: Regression 5. Dependent Variable: RATING Performed By: PEP Date: Thursday, May 04, 2006 Updating: Static Multiple R-Square Adjusted StErr of Summary R Estimate 0.7387 0.5456 0.4799 1.834 Degrees of Sum of Mean of F-Ratio p-Value ANOVA Table Freedom Squares Explained 11 306.964 27.906 8.2964 < 0.0001 Unexplained 76 255.634 3.364 Coefficient Standard t-Value Lower Upper Regression Table Error Limit Constant 12.87691 2.01203 6.3999 8.870 16.884 Fact 1.89451 0.44028 4.3029 1.018 2.771 Stars 0.74425 0.42113 1.7673 0.0812 -0.095 1.583 Prev Rating 0.18571 0.10872 1.7081 0.0917 -0.031 0.402 Competition -0.29356 0.11035 -2.6602 0.0095 -0.513 -0.074 ABN 1.07497 1.03428 1.0393 0.3019 -0.985 3.135 BBS -1.04990 0.59970 -1.7507 0.0840 -2.244 0.145 OCT -1.54061 0.68598 -2.2458 0.0276 -2.907 -0.174 DEC 1.39816 0.72802 1.9205 0.0585 -0.052 2.848 APR-MAY -1.40377 0.56574 -2.4813 0.0153 -2.531 -0.277 MON 2.52860 1.00136 2.5252 0.0136 0.534 4.523 SUN 1.52567 0.70636 2.1599 0.0339 0.119 2.933 5. A high-ranking CBC exec argued that network programming does not affect total size of network audience, only the relative share each network receives. Does the regression support or refute this assertion?

StatTools (Core Analysis Pack) Analysis: Regression 4. Dependent Variable: RATING Performed By: PEP Date: Thursday, May 04, 2006 Updating: Static Multiple R-Square Adjusted StErr of Summary R Estimate 0.5342 0.2854 0.2510 2.2008 Degrees of Sum of Mean of F-Ratio p-Value ANOVA Table Freedom Squares Explained 4 160.5680 40.1420 8.2874 < 0.0001 Unexplained 83 402.0291 4.8437 Coefficient Standard t-Value Lower Upper Regression Table Error Limit Constant 12.1471 0.4857 25.0104 11.181 13.113 Fact 2.0818 0.5044 4.1271 1.079 3.085 Stars 1.3464 0.4730 2.8466 0.0056 0.406 2.287 ABN 1.2635 0.5485 2.3036 0.0237 0.173 2.354 BBS -1.2135 0.6559 -1.8500 0.0679 -2.518 0.091 6. BBS’s new movie is fiction- based with 2 stars. We don’t know when it will be aired. Will it’s rating exceed the 1992 average for BBS movies?