Question

The following table presents the result of the logistic regression on data of students • y = \frac{e^{\beta_0 + \beta_1x_1 + \beta_2x_2}}{1 + e^{\beta_0 + \beta_1x_1 + \beta_2x_2}} + \epsilon • y: Indicator for on-time graduation, takes value 1 if the student graduated on time, 0 of not; • x?: GPA; • x?: Indicator for receiving scholarship last year, takes value 1 if received, 0 if not. Odds Ratio Intercept 0.0107 x?: gpa 4.5311 x?: scholarship 4.4760 1) (1') What is the point estimates for \(\beta_0, \beta_1, \beta_2\), respectively? 2) (1') According to the estimation result, if a student's GPA is 3.5 but did not receive the scholarship, what is her predicted probability of graduating on time?

          The following table presents the result of the logistic regression on data of students
• y = \frac{e^{\beta_0 + \beta_1x_1 + \beta_2x_2}}{1 + e^{\beta_0 + \beta_1x_1 + \beta_2x_2}} + \epsilon
• y: Indicator for on-time graduation, takes value 1 if the student graduated on time, 0 of not;
• x?: GPA;
• x?: Indicator for receiving scholarship last year, takes value 1 if received, 0 if not.
Odds Ratio
Intercept	0.0107
x?: gpa	4.5311
x?: scholarship	4.4760
1) (1') What is the point estimates for \(\beta_0, \beta_1, \beta_2\), respectively?
2) (1') According to the estimation result, if a student's GPA is 3.5 but did not receive the
scholarship, what is her predicted probability of graduating on time?

The following table presents the result of the logistic regression on data of students
• y = (e^β0 + β1x1 + β2x2)/(1 + e^β0 + β1x1 + β2x2) + ϵ• y: Indicator for on-time graduation, takes value 1 if the student graduated on time, 0 of not;
• x?: GPA;
• x?: Indicator for receiving scholarship last year, takes value 1 if received, 0 if not.
Odds Ratio
Intercept 0.0107
x?: gpa 4.5311
x?: scholarship 4.4760
1) (1') What is the point estimates for β0, β1, β2, respectively?
2) (1') According to the estimation result, if a student's GPA is 3.5 but did not receive the
scholarship, what is her predicted probability of graduating on time?

Added by Amber F.

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