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Answer :
In this question, we are dealing with multiple regression analysis, a statistical technique used to model the relationship between a dependent variable and two or more independent variables. In this context, the admissions counselor wants to relate graduate grade point averages (graduate GPA) to both undergraduate GPA and GRE scores.
The general format for a multiple regression equation is:
[tex]Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + \ldots + \beta_nX_n + \epsilon[/tex]
Where:
- Y is the dependent variable, which in this case is the graduate GPA.
- [tex]\beta_0[/tex] is the y-intercept, representing the constant term in the regression equation.
- [tex]\beta_1, \beta_2, \ldots, \beta_n[/tex] are the coefficients of the independent variables, giving the change in the dependent variable for a one-unit change in the corresponding independent variable, holding all other variables constant.
- [tex]X_1, X_2, \ldots, X_n[/tex] are the independent variables, which here are the undergraduate GPA and GRE scores.
- [tex]\epsilon[/tex] is the error term, accounting for the variability in the dependent variable that cannot be explained by the independent variables.
For this specific case, if there are only two predictors (undergraduate GPA and GRE scores), the equation would be:
[tex]\text{Graduate GPA} = \beta_0 + \beta_1 \times \text{UG"}{G}$ GPA + \beta_2 \times \text{GRE score} + \epsilon[/tex]
This equation allows the admissions counselor to predict a student's graduate GPA based on their undergraduate GPA and GRE scores by using the coefficients obtained from data analysis. This is important as it helps identify how strongly each factor impacts the graduate GPA, guiding admission decisions effectively.
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