Question

Recent years the percentage of students leave XYZ college at the end of the first year has been increased significantly. In 2019 XYZ started a two-week orientation program to help first year students to adjust the campus life. If it turns a positive effect on retention, they will consider this program is a requirement for all first year students. XYZ administration also suspects that students with less GPAs have high probability of leaving XYZ at the end of their first year. In order to investigate the relation between GPA(X1), Orientation Program(X2) on their Retention, management advised to apply the logistic regression. [For this study management selected a sample of 100 students from the last year] and observed the results. Answer the question which followed by the R output: Call: glm(formula = Y ~ X1 + X2, family = "binomial", data = LR) Deviance Residuals: Min 1Q Median 3Q Max -1.9610 -0.4828 0.2848 0.5980 1.8154 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) -6.8926 1.7472 -3.945 7.98e-05 * X1 2.5388 0.6729 3.773 0.000161 * X2 1.5608 0.5631 2.772 0.005579 --- Signif. codes: 0 '*' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 128.207 on 99 degrees of freedom Residual deviance: 80.338 on 97 degrees of freedom AIC: 86.338 Number of Fisher Scoring iterations: 5 (a)Write the logistic regression equation relating X1 and X2 to Y (b)Compute the estimated logit for independent variable X1 ,X2 (c)Comment on the overall signicance of the model? Justify by calculating Corresponding G-statistic value (d)Comment on the individual significance of the model? (e)What is the estimated odds ratio for the both GPA, Orientation Program? Comment on these values Would you recommend making the orientation program a required activity? Why or why not?

          Recent years the percentage of students leave XYZ college at the end of the first year has been increased significantly. In 2019 XYZ started a two-week orientation program to help first year students to adjust the campus life. If it turns a positive effect on retention, they will consider this program is a requirement for all first year students. XYZ administration also suspects that students with less GPAs have high probability of leaving XYZ at the end of their first year. In order to investigate the relation between GPA(X1), Orientation Program(X2) on their Retention, management advised to apply the logistic regression. [For this study management selected a sample of 100 students from the last year] and observed the results.
Answer the question which followed by the R output:
Call:
glm(formula = Y ~ X1 + X2, family = "binomial", data = LR)

Deviance Residuals:
Min 1Q Median 3Q Max
-1.9610 -0.4828 0.2848 0.5980 1.8154

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -6.8926 1.7472 -3.945 7.98e-05 ***
X1 2.5388 0.6729 3.773 0.000161 ***
X2 1.5608 0.5631 2.772 0.005579 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)
Null deviance: 128.207 on 99 degrees of freedom
Residual deviance: 80.338 on 97 degrees of freedom
AIC: 86.338

Number of Fisher Scoring iterations: 5

(a)Write the logistic regression equation relating X1 and X2 to Y
(b)Compute the estimated logit for independent variable X1 ,X2
(c)Comment on the overall signicance of the model? Justify by calculating Corresponding G-statistic value
(d)Comment on the individual significance of the model?
(e)What is the estimated odds ratio for the both GPA, Orientation Program?
Comment on these values Would you recommend making the orientation program a required activity? Why or why not?

Recent years the percentage of students leave XYZ college at the end of the first year has been increased significantly. In 2019 XYZ started a two-week orientation program to help first year students to adjust the campus life. If it turns a positive effect on retention, they will consider this program is a requirement for all first year students. XYZ administration also suspects that students with less GPAs have high probability of leaving XYZ at the end of their first year. In order to investigate the relation between GPA(X1), Orientation Program(X2) on their Retention, management advised to apply the logistic regression. [For this study management selected a sample of 100 students from the last year] and observed the results.
Answer the question which followed by the R output:
Call:
glm(formula = Y X1 + X2, family = "binomial", data = LR)

Deviance Residuals:
Min 1Q Median 3Q Max
-1.9610 -0.4828 0.2848 0.5980 1.8154

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -6.8926 1.7472 -3.945 7.98e-05 ***
X1 2.5388 0.6729 3.773 0.000161 ***
X2 1.5608 0.5631 2.772 0.005579 **
—
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)
Null deviance: 128.207 on 99 degrees of freedom
Residual deviance: 80.338 on 97 degrees of freedom
AIC: 86.338

Number of Fisher Scoring iterations: 5

(a)Write the logistic regression equation relating X1 and X2 to Y
(b)Compute the estimated logit for independent variable X1 ,X2
(c)Comment on the overall signicance of the model? Justify by calculating Corresponding G-statistic value
(d)Comment on the individual significance of the model?
(e)What is the estimated odds ratio for the both GPA, Orientation Program?
Comment on these values Would you recommend making the orientation program a required activity? Why or why not?

Added by Steven K.

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