Class 27 Example Height and Weight Case Colonial Broadcasting HBS 9894011 Heights and Weights of n30 11yearold girls CM Inches KG 135 53 26 146 57 33 153 60 55 154 61 50 139 55 32 131 52 25 ID: 766188
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Class 27 Example: Height and WeightCase: Colonial Broadcasting(HBS: 9-894-011)
Heights and Weights of n=30 11-year-old girls CM Inches KG 135 532614657331536055154615013955321315225149594413754311435636146573514156281365428154613615159481556136133523114959341415632164654714657371495946147583615260471405533143564214858321495932141562913754341355330144.80057.06736.167 Sample Means 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 Always goes thru Any three can be used to find the fourth.
Heights and Weights of n=30 11-year-old girls CM Inches KG 135 532614657331536055154615013955321315225149594413754311435636146573514156281365428154613615159481556136133523114959341415632164654714657371495946147583615260471405533143564214858321495932141562913754341355330144.80057.06736.167 Sample Means Bo regressed KG on inches. Which model will be the better predictor of KG? Al’s Bo’s They should give identical results.
AL Regression Statistics Multiple R0.742 R Square0.551 Adj R Square0.535 Standard Error5.248 Observations30 ANOVA dfSSMSFSig FRegression1946.892946.89234.3760.000003Residual28771.27427.546 Total291718.167 CoefficientsStandard Error t Stat P-value Intercept -71.371 18.366 -3.886 0.001 CM 0.743 0.127 5.863 0.000003 BO Regression Statistics Multiple R0.720 R Square0.518 Adj R Square0.501 Standard Error5.439 Observations30 ANOVA dfSSMSFSig FRegression1889.874889.87430.0820.000007Residual28828.29329.582 Total291718.167 CoefficientsStandard Errort StatP-value Intercept-66.70118.782-3.5510.001 Inches1.8030.3295.4850.000007
What if we use both?? SUMMARY OUTPUT Regression Statistics Multiple R0.760 R Square0.577 Adj R Square0.546 Standard Error5.187 Observations30 ANOVA dfSSMSFSig FRegression2991.748495.87418.4318.967E-06Residual27726.41926.904 Total291718.167 CoefficientsStandard Error 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 NetworksABN, BBS, CBCData 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 FactStarsPrev RatingCompetition1BBS1115.60114.214.52BBS1710.81015.317.2...........................19BBS11714.41112.114.220BBS11713.61011.411.921ABN1714.60019.314.422ABN1210.80116.315.2...........................57ABN12212.80016.312.058ABN12716.80115.7 10.159 CBC1 714.0 0 1 8.2 14.8 60 CBC 1 1 11.3 1 0 13.0 13.2 . . ....... ..................87CBC12111.40111.216.488CBC12119.11012.615.4Average5.884.2513.820.410.4113.7714.06Stdev3.912.852.540.490.543.232.29median4714.050013.6514.1mode4712.80013.814.4min118.9005.38.2max12719.51224.720.3
StatTools (Core Analysis Pack) Analysis:Regression 1. Dependent Variable: RATING Performed By:PEP Date:Thursday, May 04, 2006 Updating:Static MultipleR-SquareAdjustedStErr ofSummaryRR-SquareEstimate0.33800.11430.09342.4212Degrees ofSum ofMean of F-Ratiop-ValueANOVA TableFreedomSquaresSquaresExplained264.291232.145601485.48330.0058Unexplained85498.30605.862423013CoefficientStandardt-Valuep-ValueLowerUpperRegression TableErrorLimitLimitConstant13.36330.442130.2299< 0.000112.484414.2423ABN1.39720.5913 2.36270.0204 0.22142.5729 BBS-0.6483 0.6990 -0.9276 0.3563 -2.0380 0.7414 1a. Rank the networks based on average 1992 rating. 1b. How big was the ratings gap between the top and bottom ranked networks ?
StatTools (Core Analysis Pack) Analysis:Regression 2. Dependent Variable: RATING Performed By:PEP Date:Thursday, May 04, 2006 Updating:Static MultipleR-SquareAdjustedStErr ofSummaryRR-SquareEstimate0.27240.07420.06352.461Degrees ofSum ofMean of F-Ratiop-ValueANOVA TableFreedomSquaresSquaresExplained141.758241.75826.89500.0102Unexplained86520.83906.0563CoefficientStandardt-Valuep-ValueLowerUpperRegression TableErrorLimitLimitConstant13.246150.3412738.8141< 0.000112.56813.925Fact1.401070.533572.6258 0.01020.340 2.462 2a. What is the average rating of fact based movies? 2b. Is the difference in fact and fiction ratings statistically significant?
StatTools (Core Analysis Pack) Analysis:Regression 3. Dependent Variable: RATING Performed By:PEP Date:Thursday, May 04, 2006 Updating:Static MultipleR-SquareAdjustedStErr ofSummaryRR-SquareEstimate0.37330.13940.11912.387Degrees ofSum ofMean of F-Ratiop-ValueANOVA TableFreedomSquaresSquaresExplained278.42039.2106.88360.0017Unexplained85484.1775.696CoefficientStandardt-Valuep-ValueLowerUpperRegression TableErrorLimitLimitConstant12.5680.42529.550< 0.000111.7213.41Fact1.7990.541 3.3270.0013 0.722.87 Stars1.259 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 MultipleR-SquareAdjustedStErr ofSummaryRR-SquareEstimate0.73870.54560.47991.834Degrees ofSum ofMean of F-Ratiop-ValueANOVA TableFreedomSquaresSquaresExplained11306.96427.9068.2964< 0.0001Unexplained76255.6343.364CoefficientStandardt-Valuep-ValueLowerUpperRegression TableErrorLimitLimitConstant12.876912.012036.3999< 0.00018.87016.884Fact1.894510.44028 4.3029< 0.0001 1.0182.771 Stars0.74425 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 -2.66020.0095-0.513-0.074ABN1.074971.03428 1.03930.3019-0.9853.135BBS-1.049900.59970-1.75070.0840-2.2440.145OCT-1.540610.68598-2.24580.0276-2.907-0.174DEC1.398160.728021.92050.0585-0.0522.848APR-MAY-1.403770.56574-2.48130.0153-2.531-0.277MON2.528601.001362.52520.01360.5344.523SUN1.525670.706362.15990.03390.1192.9334. 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 MultipleR-SquareAdjustedStErr ofSummaryRR-SquareEstimate0.73870.54560.47991.834Degrees ofSum ofMean of F-Ratiop-ValueANOVA TableFreedomSquaresSquaresExplained11306.96427.9068.2964< 0.0001Unexplained76255.6343.364CoefficientStandardt-Valuep-ValueLowerUpperRegression TableErrorLimitLimitConstant12.876912.012036.3999< 0.00018.87016.884Fact1.894510.44028 4.3029< 0.0001 1.0182.771 Stars0.74425 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 -2.66020.0095-0.513-0.074ABN1.074971.03428 1.03930.3019-0.9853.135BBS-1.049900.59970-1.75070.0840-2.2440.145OCT-1.540610.68598-2.24580.0276-2.907-0.174DEC1.398160.728021.92050.0585-0.0522.848APR-MAY-1.403770.56574-2.48130.0153-2.531-0.277MON2.528601.001362.52520.01360.5344.523SUN1.525670.706362.15990.03390.1192.9335. 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 MultipleR-SquareAdjustedStErr ofSummaryRR-SquareEstimate0.53420.28540.25102.2008Degrees ofSum ofMean of F-Ratiop-ValueANOVA TableFreedomSquaresSquaresExplained4160.568040.14208.2874< 0.0001Unexplained83402.02914.8437CoefficientStandardt-Valuep-ValueLowerUpperRegression TableErrorLimitLimitConstant12.14710.485725.0104< 0.000111.18113.113Fact2.08180.5044 4.1271< 0.0001 1.0793.085 Stars1.3464 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 -1.85000.0679-2.5180.0916. 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?