It shows graduate program admission decisions (Yes: 1 and No: 2), GRE score and undergraduate GPA (1: ≥ 3.5 and 2: < 3.5) for fifty students. Tasks: Fit a binary logistic regression model with admission decision as the dependent variable, GRE and GPA as the independent variables. Evaluate the goodness of fit of the model. Determine the significance of independent variables. Interpret odds ratios for independent variables. State the binary logistic regression equation. Evaluate the classification accuracy of the model. Check if the residuals are independent.
Tasks:
Fit a binary logistic regression model with admission decision as the dependent variable, GRE and GPA as the independent variables.
Answer:
Goodness-of-Fit Tests :
H0 : The model is good fit
H1: The model is poor fit
The logistic regression model is statistically significant [Hosmer lemeshow test p> 0.01].that mean the null hypotehsis is fail to reject and the model is good fit The model explained 22.2% (Nagelkerke R2) of the variance in likelihood of occurrence of admission decision by GRE and GPA.
Minitab output:
Test | DF | Chi-Square | P-Value |
Deviance | 47 | 53.77 | 0.231 |
Pearson | 47 | 49.91 | 0.359 |
Hosmer-Lemeshow | 7 | 5.53 | 0.596 |
Analysis:
In our model, the first variable to analyse its impact on admission decision is the GRE score of the student. The statistical results exhibit its positive association with admission decision. With the increase in the GRE score at there is a increase in the likelihood of admission decision this is a significant explanatory variable for likelihood of admission decision in the model (p<0.01).
the second variable to analyse its impact on admission decision is the GPA score of the student, The statistical results exhibit its negative association with admission decision. The likelihood of admission decision in those student where GPA>=3.5 is 4.62 (=1/0.2162) times lesser than those wher GPA <3.5 This implies that more GPA score of the student is, more likely to take decision about admission. Hence, GPA is the significant (p=0.037< 0.05) factor for admission decision.
Output:
Coefficients
Term | Coef | SE Coef | VIF |
Constant | -3.40 | 1.53 | |
GRE | 0.00633 | 0.00252 | 1.00 |
GPA | |||
1 | -1.532 | 0.775 | 1.00 |
Deviance Table
Source | DF | Adj Dev | Adj Mean | Chi-Square | P-Value |
Regression | 2 | 15.225 | 7.613 | 15.23 | 0.000 |
GRE | 1 | 7.743 | 7.743 | 7.74 | 0.005 |
GPA | 1 | 4.354 | 4.354 | 4.35 | 0.037 |
Error | 47 | 53.769 | 1.144 | ||
Total | 49 | 68.994 |
Odds Ratios for Categorical Predictors
Level A | Level B | Odds Ratio | 95% CI |
GPA | |||
1 | 0 | 0.2162 | (0.0473, 0.9879) |
Regression Equation
P(2) | = | exp(Y')/(1 + exp(Y')) |
LOGIT (Child Mortality) = -3.402 + 0.006335 GRE -1.532 GPA
GPA | |||
0 | Y' | = | -3.402 + 0.006335 GRE |
1 | Y' | = | -4.934 + 0.006335 GRE |
It shows graduate program admission decisions (Yes: 1 and No: 2), GRE score and undergraduate GPA...
Fit a binary logistic regression model with admission decision as the dependent variable, GRE and GPA as the independent variables. Evaluate the goodness of fit of the model. Determine the significance of independent variables. Interpret odds ratios for independent variables. State the binary logistic regression equation. Evaluate the classification accuracy of the model. Check if the residuals are independent. Admit GRE GPA 0 790 1 1 370 0 1 480 1 1 580 1 1 620 1 0 740 0...
I need help interpreting logistic regression results to answer
the following question: Does GRE scores, undergraduate GPA and the
prestige (yes or no) of their undergraduate program effect
admission (yes or no) into graduate school?
Fit Group 4 Logistic Fit of ADMIT 2 By GRE 1.00 Contingency Analysis of ADMIT 2 By TOPNOTCH 2 4 Mosaic Plot Logistic Fit of ADMIT 2 By GPA 1.00 1.00 0.75 0.75 No 0.75 No No ADMIT 2 0.50 N 0.50 ADMIT 2 ADMIT...