1. Class 27 Example: Height and Weight
Case: Colonial Broadcasting (HBS: )

2. Heights and Weights of n=30 11-year-old girlsCM
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
57.067
36.167
Al used the regression of KG on CM to forecast the weight of a girl cm tall.
Al’s point forecast was _______________
Sample Means

3. 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.

4. Heights and Weights of n=30 11-year-old girlsCM
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
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

5. 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
34.376
Residual 28
27.546
Total 29
Coefficients
t Stat
P-value
Intercept
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
30.082
Residual 28
29.582
Total 29
Coefficients
t Stat
P-value
Intercept
18.782
-3.551
0.001
Inches
1.803
0.329
5.485

6. 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
18.431
8.967E-06
Residual 27
26.904
Total 29
Coefficients
t Stat
P-value
Intercept
18.187
-4.005
0.0004 CM
2.180
1.121
1.946
0.0621
Inches
-3.623
2.806
-1.291
0.2076

7. Which Girl was most over(under)weight?

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

9. 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.

11. . 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

12. 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
5.4833
0.0058
Unexplained 85
Coefficient
Standard
t-Value
Lower
Upper
Regression Table
Error
Limit
Constant
0.4421
<
ABN
1.3972
0.5913
2.3627
0.0204
0.2214
2.5729
BBS
0.6990
0.3563
0.7414
1b. How big was the ratings gap between the top and bottom ranked networks?

13. 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
6.8950
0.0102
Unexplained 86
6.0563
Coefficient
Standard
t-Value
Lower
Upper
Regression Table
Error
Limit
Constant
<
12.568
13.925
Fact
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?

14. 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
5.696
Coefficient
Standard
t-Value
Lower
Upper
Regression Table
Error
Limit
Constant
12.568
0.425
29.550
<
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.

15. 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
27.906
8.2964
<
Unexplained 76
3.364
Coefficient
Standard
t-Value
Lower
Upper
Regression Table
Error
Limit
Constant
6.3999
8.870
16.884
Fact
4.3029
1.018
2.771
Stars
1.7673
0.0812
-0.095
1.583
Prev Rating
1.7081
0.0917
-0.031
0.402
Competition
0.0095
-0.513
-0.074
ABN
1.0393
0.3019
-0.985
3.135
BBS
0.0840
-2.244
0.145
OCT
0.0276
-2.907
-0.174
DEC
1.9205
0.0585
-0.052
2.848
APR-MAY
0.0153
-2.531
-0.277
MON
2.5252
0.0136
0.534
4.523
SUN
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?

16. 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
27.906
8.2964
<
Unexplained 76
3.364
Coefficient
Standard
t-Value
Lower
Upper
Regression Table
Error
Limit
Constant
6.3999
8.870
16.884
Fact
4.3029
1.018
2.771
Stars
1.7673
0.0812
-0.095
1.583
Prev Rating
1.7081
0.0917
-0.031
0.402
Competition
0.0095
-0.513
-0.074
ABN
1.0393
0.3019
-0.985
3.135
BBS
0.0840
-2.244
0.145
OCT
0.0276
-2.907
-0.174
DEC
1.9205
0.0585
-0.052
2.848
APR-MAY
0.0153
-2.531
-0.277
MON
2.5252
0.0136
0.534
4.523
SUN
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?

17. 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
8.2874
<
Unexplained 83
4.8437
Coefficient
Standard
t-Value
Lower
Upper
Regression Table
Error
Limit
Constant
0.4857
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
0.6559
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?