Question

8 Problem 8 A study of 170 franchise firms classified each firm as to whether it was successful or not. Attached is the data Observed numbers of firms Exclusive territory No 15 Success es Total 108 34 123 47 CS No 13 Total 142 28 170 1. (2 points) What proportion of exclusive territory firms are successful? 2. (2 points) Find the log odds for the answer in part 1.) 3. (6 points) Let x1 for exclusive territories and r -0 for other territories. Using R or otherwise. (a) (3 points) The fitted logistic regression model (b) (3 points) Odds ratio for exclusive territory versus no exclusive territory.

Answer 1

sol:

142 170 0.8353

odds(success) = = 2.7529 Odds ratio -odds(No)

Therefore log-odds=1.0127

————— 05-04-2019 21:27:51 ————————————————————

Welcome to Minitab, press F1 for help.

Binary Logistic Regression: Y versus X

Method

Link function Logit
Categorical predictor coding (1, 0)
Rows used 170

Response Information

Variable Value Count
Y 1 123 (Event)
0 47
Total 170

Deviance Table

Source DF Adj Dev Adj Mean Chi-Square P-Value
Regression 1 5.465 5.465 5.46 0.019
X 1 5.465 5.465 5.46 0.019
Error 168 194.995 1.161
Total 169 200.460

Model Summary

Deviance Deviance
R-Sq R-Sq(adj) AIC
2.73% 2.23% 199.00

Coefficients

Term Coef SE Coef VIF
Constant 0.143 0.379
X
1 1.013 0.427 1.00

Odds Ratios for Categorical Predictors

Level A Level B Odds Ratio 95% CI
X
1 0 2.7529 (1.1923, 6.3561)

Odds ratio for level A relative to level B

Regression Equation

P(1) = exp(Y')/(1 + exp(Y'))

Y' = 0.143 + 0.0 X_0 + 1.013 X_1

Goodness-of-Fit Tests

Test DF Chi-Square P-Value
Deviance 168 195.00 0.075
Pearson 168 170.00 0.442
Hosmer-Lemeshow 0 0.00 *

Fits and Diagnostics for Unusual Observations

Observed
Obs Probability Fit Resid Std Resid
143 1.0000 0.5357 1.1173 1.14 X
144 1.0000 0.5357 1.1173 1.14 X
145 1.0000 0.5357 1.1173 1.14 X
146 1.0000 0.5357 1.1173 1.14 X
147 1.0000 0.5357 1.1173 1.14 X
148 1.0000 0.5357 1.1173 1.14 X
149 1.0000 0.5357 1.1173 1.14 X
150 1.0000 0.5357 1.1173 1.14 X
151 1.0000 0.5357 1.1173 1.14 X
152 1.0000 0.5357 1.1173 1.14 X
153 1.0000 0.5357 1.1173 1.14 X
154 1.0000 0.5357 1.1173 1.14 X
155 1.0000 0.5357 1.1173 1.14 X
156 1.0000 0.5357 1.1173 1.14 X
157 1.0000 0.5357 1.1173 1.14 X
158 0.0000 0.5357 -1.2388 -1.26 X
159 0.0000 0.5357 -1.2388 -1.26 X
160 0.0000 0.5357 -1.2388 -1.26 X
161 0.0000 0.5357 -1.2388 -1.26 X
162 0.0000 0.5357 -1.2388 -1.26 X
163 0.0000 0.5357 -1.2388 -1.26 X
164 0.0000 0.5357 -1.2388 -1.26 X
165 0.0000 0.5357 -1.2388 -1.26 X
166 0.0000 0.5357 -1.2388 -1.26 X
167 0.0000 0.5357 -1.2388 -1.26 X
168 0.0000 0.5357 -1.2388 -1.26 X
169 0.0000 0.5357 -1.2388 -1.26 X
170 0.0000 0.5357 -1.2388 -1.26 X

X Unusual X

142 170 0.8353

odds(success) = = 2.7529 Odds ratio -odds(No)

Therefore log-odds=1.0127

————— 05-04-2019 21:27:51 ————————————————————

Welcome to Minitab, press F1 for help.

Binary Logistic Regression: Y versus X

Method

Link function Logit
Categorical predictor coding (1, 0)
Rows used 170

Response Information

Variable Value Count
Y 1 123 (Event)
0 47
Total 170

Deviance Table

Source DF Adj Dev Adj Mean Chi-Square P-Value
Regression 1 5.465 5.465 5.46 0.019
X 1 5.465 5.465 5.46 0.019
Error 168 194.995 1.161
Total 169 200.460

Model Summary

Deviance Deviance
R-Sq R-Sq(adj) AIC
2.73% 2.23% 199.00

Coefficients

Term Coef SE Coef VIF
Constant 0.143 0.379
X
1 1.013 0.427 1.00

Odds Ratios for Categorical Predictors

Level A Level B Odds Ratio 95% CI
X
1 0 2.7529 (1.1923, 6.3561)

Odds ratio for level A relative to level B

Regression Equation

P(1) = exp(Y')/(1 + exp(Y'))

Y' = 0.143 + 0.0 X_0 + 1.013 X_1

Goodness-of-Fit Tests

Test DF Chi-Square P-Value
Deviance 168 195.00 0.075
Pearson 168 170.00 0.442
Hosmer-Lemeshow 0 0.00 *

Fits and Diagnostics for Unusual Observations

Observed
Obs Probability Fit Resid Std Resid
143 1.0000 0.5357 1.1173 1.14 X
144 1.0000 0.5357 1.1173 1.14 X
145 1.0000 0.5357 1.1173 1.14 X
146 1.0000 0.5357 1.1173 1.14 X
147 1.0000 0.5357 1.1173 1.14 X
148 1.0000 0.5357 1.1173 1.14 X
149 1.0000 0.5357 1.1173 1.14 X
150 1.0000 0.5357 1.1173 1.14 X
151 1.0000 0.5357 1.1173 1.14 X
152 1.0000 0.5357 1.1173 1.14 X
153 1.0000 0.5357 1.1173 1.14 X
154 1.0000 0.5357 1.1173 1.14 X
155 1.0000 0.5357 1.1173 1.14 X
156 1.0000 0.5357 1.1173 1.14 X
157 1.0000 0.5357 1.1173 1.14 X
158 0.0000 0.5357 -1.2388 -1.26 X
159 0.0000 0.5357 -1.2388 -1.26 X
160 0.0000 0.5357 -1.2388 -1.26 X
161 0.0000 0.5357 -1.2388 -1.26 X
162 0.0000 0.5357 -1.2388 -1.26 X
163 0.0000 0.5357 -1.2388 -1.26 X
164 0.0000 0.5357 -1.2388 -1.26 X
165 0.0000 0.5357 -1.2388 -1.26 X
166 0.0000 0.5357 -1.2388 -1.26 X
167 0.0000 0.5357 -1.2388 -1.26 X
168 0.0000 0.5357 -1.2388 -1.26 X
169 0.0000 0.5357 -1.2388 -1.26 X
170 0.0000 0.5357 -1.2388 -1.26 X

X Unusual X