The SAT and ACT exams are often used to predict a student's first-term college grade point average (GPA). Different formulas are used for different colleges and majors. Suppose that a student is applying to a university with an intended major in civil engineering. Also suppose that for this college and this major, the following model is used to predict first term GPA. GPA= a+ b(ACT)
a= 0.4
b= 0.3

Requried:
a. In this context, what would be the appropriate interpretation of the value of a?
b. In this context, what would be the appropriate interpretation of the value of b?

In this example it seems that "a" is a fixed value that is added to adjust the scale value. . It seems that "b" is a factor that adjust the value of the ACT score as a predictor for success in the chosen field of study.

Step-by-step explanation: The scores from the SAT and ACT are not in the same format as GPA. So the scale needs adjustment. Also the tests measure different knowledge and skills. They may be more or less reliable as predictors of success in a given field of study, so the "b" factor would change for different majors.

Based on the context ;

a = lowest GPA value a student can according to the model.

b = change in GPA value per unit change in ACT score.

The given relationship between GPA and ACT Score is a simple linear regression model in the form :

y = bx + c

Where ; y = Predicted value ; b = slope or gradient ; c = intercept

GPA prediction model:

GPA = a + b(ACT)

Comparing the general linear regression model with the GPA model given :

b = slope = change in y per unit change in x;

• Based on the context, this means ;Change in GPA value per unit change in ACT Score

a = intercept = value of y when x = 0;

• Based on the context, a is the lowest GPA value a student can have. (even if such student has an ACT Score of 0).

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