A logistic regression model is developed with the the response variable, Y, being whether or not A football wins (Y = 1 if we win and 0 if we lose). The predictors are A win% A had won going the percent of the previous ten games that into the game in question, ranging from 0 to 100 same definition for the opponent's last 10 games an indicator variable with 1 corresponding to a and 0 an away game Opp Win% Home? A home game Temperature the temperature at which the game was played Below are the outputs for the logistic regression. Coef SE Coef ChiSquare P-value -25.3 10.54 Constant A Win% Opp Win% 5.76 0.0164 0.466 0.176 7.01 0.0081 -0.17 0.643 0.07 0.7915

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A logistic regression model is developed with the the response variable, Y, being whether
or not
A football wins (Y = 1 if we win and 0 if we lose). The predictors are
A Win%
the percent of the previous ten games that A had won going
into the game in question, ranging from 0 to 100
same definition for the opponent's last 10 games
an indicator variable with 1 corresponding to a A home game
and 0 an away game
Opp Win%
Home?
Temperature the temperature at which the game was played
Below are the outputs for the logistic regression.
Coef
SE Coef ChiSquare
P-value
-25.3 10.54
Constant
A Win%
Opp Win%
5.76
0.0164
0.466 0.176
7.01
0.0081
-0.17 0.643
0.07
0.7915
Home?
1.45
0.660
4.83
0.0280
Temperature 0.115 0.045
6.53
0.0106
(1) Which predictors are significant at 5% significance level?
(2) Does it make sense that the coefficient for Opp Win% is negative? Explain.
(3) What does the coefficient for Temperature tell us about the relationship between
temperature and the probability that Rutgers wins? Compute the corresponding
odds ratio for a 1 degree increase in temperature and explain what it means.
(4) Estimate the probability of A winning a game against B
played in
B at 50 degrees temperature where both teams have a winning percentage
of 70.
Transcribed Image Text:A logistic regression model is developed with the the response variable, Y, being whether or not A football wins (Y = 1 if we win and 0 if we lose). The predictors are A Win% the percent of the previous ten games that A had won going into the game in question, ranging from 0 to 100 same definition for the opponent's last 10 games an indicator variable with 1 corresponding to a A home game and 0 an away game Opp Win% Home? Temperature the temperature at which the game was played Below are the outputs for the logistic regression. Coef SE Coef ChiSquare P-value -25.3 10.54 Constant A Win% Opp Win% 5.76 0.0164 0.466 0.176 7.01 0.0081 -0.17 0.643 0.07 0.7915 Home? 1.45 0.660 4.83 0.0280 Temperature 0.115 0.045 6.53 0.0106 (1) Which predictors are significant at 5% significance level? (2) Does it make sense that the coefficient for Opp Win% is negative? Explain. (3) What does the coefficient for Temperature tell us about the relationship between temperature and the probability that Rutgers wins? Compute the corresponding odds ratio for a 1 degree increase in temperature and explain what it means. (4) Estimate the probability of A winning a game against B played in B at 50 degrees temperature where both teams have a winning percentage of 70.
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