Team Winning Percentage Runs Home Runs Team Batting Average On Base Percentage B
ID: 3318753 • Letter: T
Question
Team
Winning Percentage
Runs
Home Runs
Team Batting Average
On Base Percentage
Batting Average Against
Team ERA
Philadelphia
0.599
772
166
0.260
0.332
0.254
3.67
Atlanta
0.562
738
139
0.258
0.339
0.246
3.56
San Francisco
0.568
697
162
0.257
0.321
0.236
3.36
Chicago Cubs
0.463
685
149
0.257
0.320
0.255
4.18
Florida
0.494
719
152
0.254
0.321
0.261
4.08
LA Dodgers
0.494
667
120
0.252
0.322
0.244
4.01
Washington
0.426
655
149
0.250
0.318
0.266
4.13
Arizona
0.401
713
180
0.250
0.325
0.271
4.81
NY Mets
0.488
656
128
0.249
0.314
0.260
3.70
Houston
0.469
611
108
0.247
0.303
0.261
4.09
San Diego
0.556
665
132
0.246
0.317
0.240
3.39
Pittsburgh
0.352
587
126
0.242
0.304
0.282
5.00
Some of these variables make better predictor variables and some make better response variables. Spend some time thinking about what you suspect could be pairs of response and explanatory (predictor) variables.
1) For which pair of variables is a least squares regression model inappropriate? (5 points)
2) Now focus on a pair of variables that is best fit for a least squares regression model/equation. (8 points)
a) How did you decide on this pair of variables?
b) Which variable should be the explanatory variable, and which should be the response variable? Explain your choices.
c) What is the least squares regression model and what statistical support do you have that this model has any value?
3) Consider your least squares regression model/equation. (7 points)
a) Interpret the slope of your model.
b) Interpret the intercept of your model, and if the interpretation is inappropriate, explain why.
c) Between what two values of the predictor variable is your model valid?
d) Explain why extrapolation (using values outside of the scope of the model) could be dangerous.
e) Give a specific example of a prediction that could be made with your model, and interpret your answer.
f) Describe any other limitations of your model.
Team
Winning Percentage
Runs
Home Runs
Team Batting Average
On Base Percentage
Batting Average Against
Team ERA
Philadelphia
0.599
772
166
0.260
0.332
0.254
3.67
Atlanta
0.562
738
139
0.258
0.339
0.246
3.56
San Francisco
0.568
697
162
0.257
0.321
0.236
3.36
Chicago Cubs
0.463
685
149
0.257
0.320
0.255
4.18
Florida
0.494
719
152
0.254
0.321
0.261
4.08
LA Dodgers
0.494
667
120
0.252
0.322
0.244
4.01
Washington
0.426
655
149
0.250
0.318
0.266
4.13
Arizona
0.401
713
180
0.250
0.325
0.271
4.81
NY Mets
0.488
656
128
0.249
0.314
0.260
3.70
Houston
0.469
611
108
0.247
0.303
0.261
4.09
San Diego
0.556
665
132
0.246
0.317
0.240
3.39
Pittsburgh
0.352
587
126
0.242
0.304
0.282
5.00
Explanation / Answer
1)
Winning Percentage
Runs
Home Runs
Team Batting Average
On Base Percentage
Batting Average Against
Team ERA
Winning Percentage
1
Runs
0.6523
1
Home Runs
0.1290
0.7086
1.0000
Team Batting Average
0.6663
0.8575
0.5319
1.0000
On Base Percentage
0.5875
0.9150
0.5762
0.8030
1.0000
Batting Average Against
-0.8503
-0.4092
0.0145
-0.5212
-0.4517
1.0000
Team ERA
-0.9186
-0.4166
0.0456
-0.4904
-0.4020
0.8796
1
One of the main assumptions of regression analysis is that dependent and the independent variables are linearly related to each other. There is a weak linear relationship between two variables if the value of correlation Coefficient lies between (-0.3, 0.3). Hence for pairs (Winning Percentage, Home Runs) (Home Runs, Batting Average Against) and (Home Runs, Team ERA) least squares regression model inappropriate
Winning Percentage
Runs
Home Runs
Team Batting Average
On Base Percentage
Batting Average Against
Team ERA
Winning Percentage
1
Runs
0.6523
1
Home Runs
0.1290
0.7086
1.0000
Team Batting Average
0.6663
0.8575
0.5319
1.0000
On Base Percentage
0.5875
0.9150
0.5762
0.8030
1.0000
Batting Average Against
-0.8503
-0.4092
0.0145
-0.5212
-0.4517
1.0000
Team ERA
-0.9186
-0.4166
0.0456
-0.4904
-0.4020
0.8796
1
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