Class 27 Example Height and Weight Case Colonial

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

Heights and Weights of n=30 11 -year-old girls CM 135 146 153 154 139 131 149 137 143 146 141 136 154 151 155 133 149 141 164 146 149 147 152 140 143 148 149 141 137 135 144. 800 Sample Means Inches 53 57 60 61 55 52 59 54 56 57 56 54 61 59 61 52 59 56 65 57 59 58 60 55 56 58 59 56 54 53 57. 067 KG 26 33 55 50 32 25 44 31 36 35 28 28 36 48 36 31 34 32 47 37 46 36 47 33 42 32 32 29 34 30 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 ________

The regression line Any three can be used to find the fourth.

Heights and Weights of n=30 11 -year-old girls CM 135 146 153 154 139 131 149 137 143 146 141 136 154 151 155 133 149 141 164 146 149 147 152 140 143 148 149 141 137 135 144. 800 Sample Means Inches 53 57 60 61 55 52 59 54 56 57 56 54 61 59 61 52 59 56 65 57 59 58 60 55 56 58 59 56 54 53 57. 067 KG 26 33 55 50 32 25 44 31 36 35 28 28 36 48 36 31 34 32 47 37 46 36 47 33 42 32 32 29 34 30 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.

AL BO Regression Statistics Multiple R 0. 742 R Square 0. 551 Adj R Square 0. 535 Standard Error 5. 248 Observations 30 Regression Statistics Multiple R 0. 720 R Square 0. 518 Adj R Square 0. 501 Standard Error 5. 439 Observations 30 ANOVA df Regression Residual Total Intercept CM 1 28 29 SS MS 946. 892 771. 274 27. 546 1718. 167 F Sig F 34. 376 0. 000003 Coefficients Standard Error t Stat P-value -71. 371 18. 366 -3. 886 0. 001 0. 743 0. 127 5. 863 0. 000003 df Regression Residual Total Intercept Inches 1 28 29 SS MS 889. 874 828. 293 29. 582 1718. 167 F Sig F 30. 082 0. 000007 Coefficients Standard Error t Stat P-value -66. 701 18. 782 -3. 551 0. 001 1. 803 0. 329 5. 485 0. 000007

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 Regression Residual Total Intercept CM Inches 2 27 29 SS MS 991. 748 495. 874 726. 419 26. 904 1718. 167 F Sig F 18. 431 8. 967 E-06 Coefficients Standard Error t Stat P-value -72. 836 18. 187 -4. 005 0. 0004 2. 180 1. 121 1. 946 0. 0621 -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 1 2 Network BBS Month 1 1 Day 1 7 Rating 15. 6 10. 8 Fact Stars 0 1 1 0 Prev Rating 14. 2 15. 3 Competition 14. 5 17. 2 . . . . 19 20 21 22 BBS ABN 11 11 1 1 7 7 7 2 14. 4 13. 6 14. 6 10. 8 1 1 0 0 1 12. 1 11. 4 19. 3 16. 3 14. 2 11. 9 14. 4 15. 2 . . . . 57 58 59 60 ABN CBC 12 12 1 1 2 7 7 1 12. 8 16. 8 14. 0 11. 3 0 0 0 1 1 0 16. 3 15. 7 8. 2 13. 0 12. 0 10. 1 14. 8 13. 2 . . . . 87 88 Average Stdev median mode min max CBC 12 12 5. 88 3. 91 4 4 1 12 1 1 4. 25 2. 85 7 7 11. 4 19. 1 13. 82 2. 54 14. 05 12. 8 8. 9 19. 5 0 1 0. 49 0 0 0 1 1 0 0. 41 0. 54 0 0 0 2 11. 2 12. 6 13. 77 3. 23 13. 65 13. 8 5. 3 24. 7 16. 4 15. 4 14. 06 2. 29 14. 1 14. 4 8. 2 20. 3

Stat. Tools(Core Analysis Pack) 1 a. Rank the networks based on average 1992 rating. Analysis: Regression 1. Dependent Variable: RATING Performed By: PEP Date: Thursday, May 04, 2006 Updating: Static Multiple Summary ANOVA Table Explained Unexplained Regression Table R R-Square Adjusted St. Err of R-Square Estimate 2. 4212 0. 3380 0. 1143 0. 0934 Degrees of Sum of Mean of Freedom Squares 2 64. 2912 32. 14560148 85 498. 3060 5. 862423013 Coefficient Standard Error t-Value F-Ratio p-Value 5. 4833 0. 0058 p-Value Lower Upper Limit 13. 3633 0. 4421 30. 2299 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 Constant < 0. 0001 12. 4844 14. 2423 1 b. How big was the ratings gap between the top and bottom ranked networks?

Stat. Tools(Core Analysis Pack) 2 a. What is the average rating of fact based movies? Analysis: Regression 2. Dependent Variable: RATING Performed By: PEP Date: Thursday, May 04, 2006 Updating: Static Multiple Summary ANOVA Table Explained Unexplained Regression Table Constant Fact R R-Square Adjusted St. Err of R-Square Estimate 2. 461 0. 2724 0. 0742 0. 0635 Degrees of Sum of Mean of Freedom Squares 1 86 41. 7582 520. 8390 Coefficient 13. 24615 1. 40107 Standard Error 0. 34127 0. 53357 F-Ratio p-Value 41. 7582 6. 0563 6. 8950 0. 0102 t-Value p-Value 38. 8141 2. 6258 < 0. 0001 0. 0102 Lower Upper Limit 12. 568 13. 925 0. 340 2. 462 2 b. Is the difference in fact and fiction ratings statistically significant?

Stat. Tools(Core Analysis Pack) 3. Which is most true? Analysis: Regression 3. Dependent Variable: RATING Performed By: PEP Date: Thursday, May 04, 2006 a. fact-based movies had fewer stars (than fictional movies) Updating: Static Multiple Summary ANOVA Table Explained Unexplained Stars St. Err of Estimate 2. 387 0. 1394 0. 1191 Degrees of Sum of Mean of Freedom Squares 2 85 78. 420 484. 177 Regression Table Fact Adjusted R-Square 0. 3733 Coefficient Constant R-Square R Standard F-Ratio p-Value 39. 210 5. 696 6. 8836 0. 0017 t-Value p-Value 29. 550 3. 327 2. 537 < 0. 0001 0. 0013 0. 0130 Error 12. 568 1. 799 1. 259 0. 425 0. 541 0. 496 Lower b. Fact-based movies had more stars. Upper Limit 11. 72 0. 27 13. 41 2. 87 2. 24 c. Fact-based movies had the same number of stars. d. Cannont be determined.

Stat. Tools(Core Analysis Pack) Regression 5. Dependent Variable: Analysis: RATING Performed By: PEP Date: Thursday, May 04, 2006 Updating: Static Multiple Summary ANOVA Table Explained Unexplained Regression Table Constant Fact Stars Prev Rating Competition ABN BBS OCT DEC APR-MAY MON SUN R R-Square Adjusted St. Err of R-Square Estimate 1. 834 0. 7387 0. 5456 0. 4799 Degrees of Sum of Mean of Freedom Squares 11 76 306. 964 255. 634 Coefficient 12. 87691 1. 89451 0. 74425 0. 18571 -0. 29356 1. 07497 -1. 04990 -1. 54061 1. 39816 -1. 40377 2. 52860 1. 52567 Standard Error 2. 01203 0. 44028 0. 42113 0. 10872 0. 11035 1. 03428 0. 59970 0. 68598 0. 72802 0. 56574 1. 00136 0. 70636 F-Ratio p-Value 27. 906 3. 364 8. 2964 < 0. 0001 t-Value p-Value 6. 3999 4. 3029 1. 7673 1. 7081 -2. 6602 1. 0393 -1. 7507 -2. 2458 1. 9205 -2. 4813 2. 5252 2. 1599 < 0. 0001 0. 0812 0. 0917 0. 0095 0. 3019 0. 0840 0. 0276 0. 0585 0. 0153 0. 0136 0. 0339 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? Lower Upper Limit 8. 870 16. 884 1. 018 2. 771 -0. 095 1. 583 -0. 031 0. 402 -0. 513 -0. 074 -0. 985 3. 135 -2. 244 0. 145 -2. 907 -0. 174 -0. 052 2. 848 -2. 531 -0. 277 0. 534 4. 523 0. 119 2. 933

Stat. Tools(Core Analysis Pack) Regression 5. Dependent Variable: Analysis: RATING Performed By: PEP Date: Thursday, May 04, 2006 Updating: Static Multiple Summary ANOVA Table Explained Unexplained Regression Table Constant Fact Stars Prev Rating Competition ABN BBS OCT DEC APR-MAY MON SUN R R-Square Adjusted St. Err of R-Square Estimate 1. 834 0. 7387 0. 5456 0. 4799 Degrees of Sum of Mean of Freedom Squares 11 76 306. 964 255. 634 Coefficient 12. 87691 1. 89451 0. 74425 0. 18571 -0. 29356 1. 07497 -1. 04990 -1. 54061 1. 39816 -1. 40377 2. 52860 1. 52567 Standard Error 2. 01203 0. 44028 0. 42113 0. 10872 0. 11035 1. 03428 0. 59970 0. 68598 0. 72802 0. 56574 1. 00136 0. 70636 F-Ratio p-Value 27. 906 3. 364 8. 2964 < 0. 0001 t-Value p-Value 6. 3999 4. 3029 1. 7673 1. 7081 -2. 6602 1. 0393 -1. 7507 -2. 2458 1. 9205 -2. 4813 2. 5252 2. 1599 < 0. 0001 0. 0812 0. 0917 0. 0095 0. 3019 0. 0840 0. 0276 0. 0585 0. 0153 0. 0136 0. 0339 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? Lower Upper Limit 8. 870 16. 884 1. 018 2. 771 -0. 095 1. 583 -0. 031 0. 402 -0. 513 -0. 074 -0. 985 3. 135 -2. 244 0. 145 -2. 907 -0. 174 -0. 052 2. 848 -2. 531 -0. 277 0. 534 4. 523 0. 119 2. 933

Stat. Tools(Core Analysis Pack) 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? Analysis: Regression 4. Dependent Variable: RATING Performed By: PEP Date: Thursday, May 04, 2006 Updating: Static Multiple Summary ANOVA Table Explained Unexplained Regression Table Constant Fact Stars ABN BBS R R-Square Adjusted St. Err of R-Square Estimate 0. 5342 0. 2854 0. 2510 Degrees of Sum of Mean of Freedom Squares 4 83 160. 5680 402. 0291 Coefficient 12. 1471 2. 0818 1. 3464 1. 2635 -1. 2135 Standard Error 0. 4857 0. 5044 0. 4730 0. 5485 0. 6559 2. 2008 F-Ratio p-Value 40. 1420 8. 2874 < 0. 0001 4. 8437 t-Value 25. 0104 4. 1271 2. 8466 2. 3036 -1. 8500 p-Value Lower Upper Limit < 0. 0001 11. 181 13. 113 < 0. 0001 1. 079 3. 085 0. 0056 0. 406 2. 287 0. 0237 0. 173 2. 354 0. 0679 -2. 518 0. 091