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

Class 27Example: Height and WeightCase: Colonial Broadcasting

(HBS: 9-894-011)

Heights and Weights of n=30 11-year-old girlsCM Inches KG135 53 26146 57 33153 60 55154 61 50139 55 32131 52 25149 59 44137 54 31143 56 36146 57 35141 56 28136 54 28154 61 36151 59 48155 61 36133 52 31149 59 34141 56 32164 65 47146 57 37149 59 46147 58 36152 60 47140 55 33143 56 42148 58 32149 59 32141 56 29137 54 34135 53 30

144.800 57.067 36.167

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 _______________

𝑌=�̂�+ �̂� 𝑋

𝑌=�̂�+ �̂� 𝑋

The regression line

Always goes thru Any three can

be used to find the fourth.

Heights and Weights of n=30 11-year-old girlsCM Inches KG135 53 26146 57 33153 60 55154 61 50139 55 32131 52 25149 59 44137 54 31143 56 36146 57 35141 56 28136 54 28154 61 36151 59 48155 61 36133 52 31149 59 34141 56 32164 65 47146 57 37149 59 46147 58 36152 60 47140 55 33143 56 42148 58 32149 59 32141 56 29137 54 34135 53 30

144.800 57.067 36.167

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 R 0.742 R Square 0.551 Adj R Square 0.535 Standard Error 5.248 Observations 30 ANOVA

df SS MS F Sig FRegression 1 946.892 946.892 34.376 0.000003Residual 28 771.274 27.546 Total 29 1718.167

Coefficients Standard Error t Stat P-value Intercept -71.371 18.366 -3.886 0.001 CM 0.743 0.127 5.863 0.000003

BO


df SS MS F Sig FRegression 1 889.874 889.874 30.082 0.000007Residual 28 828.293 29.582 Total 29 1718.167

Coefficients Standard Error t Stat P-value Intercept -66.701 18.782 -3.551 0.001 Inches 1.803 0.329 5.485 0.000007

What if we use both??SUMMARY OUTPUT


df SS MS F Sig FRegression 2 991.748 495.874 18.431 8.967E-06Residual 27 726.419 26.904 Total 29 1718.167

Coefficients Standard 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 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 Competition1 BBS 1 1 15.6 0 1 14.2 14.52 BBS 1 7 10.8 1 0 15.3 17.2

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .19 BBS 11 7 14.4 1 1 12.1 14.220 BBS 11 7 13.6 1 0 11.4 11.921 ABN 1 7 14.6 0 0 19.3 14.422 ABN 1 2 10.8 0 1 16.3 15.2

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .57 ABN 12 2 12.8 0 0 16.3 12.058 ABN 12 7 16.8 0 1 15.7 10.159 CBC 1 7 14.0 0 1 8.2 14.860 CBC 1 1 11.3 1 0 13.0 13.2

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .87 CBC 12 1 11.4 0 1 11.2 16.4

88 CBC 12 1 19.1 1 0 12.6 15.4Average 5.88 4.25 13.82 0.41 0.41 13.77 14.06

Stdev 3.91 2.85 2.54 0.49 0.54 3.23 2.29median 4 7 14.05 0 0 13.65 14.1mode 4 7 12.8 0 0 13.8 14.4min 1 1 8.9 0 0 5.3 8.2max 12 7 19.5 1 2 24.7 20.3

StatTools(Core Analysis Pack)

Analysis:Regression 1. Dependent Variable: RATING

Performed By:PEP

Date:Thursday, May 04, 2006

Updating:Static

MultipleR-Square

Adjusted StErr of

Summary R R-Square Estimate

0.3380 0.1143 0.0934 2.4212

Degrees of Sum of Mean of F-Ratio p-Value

ANOVA Table Freedom Squares Squares

Explained 2 64.2912 32.14560148 5.4833 0.0058

Unexplained 85 498.3060 5.862423013

CoefficientStandard

t-Value p-ValueLower Upper

Regression Table Error Limit 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

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-Square

Adjusted StErr of


0.2724 0.0742 0.0635 2.461



Explained 1 41.7582 41.7582 6.8950 0.0102

Unexplained 86 520.8390 6.0563

CoefficientStandard



Constant 13.24615 0.34127 38.8141 < 0.0001 12.568 13.925

Fact 1.40107 0.53357 2.6258 0.0102 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?



Performed By:PEP


Updating:Static

MultipleR-Square

Adjusted StErr of


0.3733 0.1394 0.1191 2.387



Explained 2 78.420 39.210 6.8836 0.0017

Unexplained 85 484.177 5.696

CoefficientStandard



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?

a. fact-based movies had fewer stars (than fictional movies)

b. Fact-based movies had more stars.

c. Fact-based movies had the same number of stars.

d. Cannont be determined.



Performed By:PEP


Updating:Static

MultipleR-Square

Adjusted StErr of


0.7387 0.5456 0.4799 1.834



Explained 11 306.964 27.906 8.2964 < 0.0001

Unexplained 76 255.634 3.364

CoefficientStandard



Constant 12.87691 2.01203 6.3999 < 0.0001 8.870 16.884

Fact 1.89451 0.44028 4.3029 < 0.0001 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?



Performed By:PEP


Updating:Static

MultipleR-Square

Adjusted StErr of


0.7387 0.5456 0.4799 1.834



Explained 11 306.964 27.906 8.2964 < 0.0001

Unexplained 76 255.634 3.364

CoefficientStandard



Constant 12.87691 2.01203 6.3999 < 0.0001 8.870 16.884

Fact 1.89451 0.44028 4.3029 < 0.0001 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

MultipleR-Square

Adjusted StErr of


0.5342 0.2854 0.2510 2.2008



Explained 4 160.5680 40.1420 8.2874 < 0.0001

Unexplained 83 402.0291 4.8437

CoefficientStandard



Constant 12.1471 0.4857 25.0104 < 0.0001 11.181 13.113

Fact 2.0818 0.5044 4.1271 < 0.0001 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?

Documents

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