The multiple regression describes how the mean value of y is related to the xi independent variables. The parameters ?i are used to describe how the mean value of y changes for a one-unit increase in xi when the other variables are held constant. The given estimated regression equation follows where x1 is the high-school grade point average, x2 is the SAT mathematics score, and y is the final college grade point average. ŷ = −1.38 + 0.0232x1 + 0.00482x2 If the variable x2 is held constant, then only changes in x1 will impact the predicted values of ŷ. Since the coefficient of x1 is positive, for each one-unit increase of x1, the values of ŷ will increase by the value of ?1, where ?1 = . In context, for each one point increase of the high-school grade point average, the final college grade point average will increase by this amount when the SAT mathematics score does not change. If the variable x1 is held constant, then only changes in x2 will impact the predicted values of ŷ. Since the coefficient of x2 is positive, for each one-unit increase of x2, the values of ŷ will increase by the value of ?2, where ?2 = . In context, for each one point increase of the SAT mathematics score, the final college grade point average will increase by this amount when the high-school grade point average does not change.
The multiple regression describes how the
?i
are used to describe how the mean value of y changes for a one-unit increase in xi when the other variables are held constant.
The given estimated regression equation follows where x1 is the high-school grade point average, x2 is the SAT mathematics score, and y is the final college grade point average.
ŷ = −1.38 + 0.0232x1 + 0.00482x2
If the variable x2 is held constant, then only changes in x1 will impact the predicted values of ŷ. Since the coefficient of x1 is positive, for each one-unit increase of x1, the values of ŷ will increase by the value of ?1, where
?1 = .
In context, for each one point increase of the high-school grade point average, the final college grade point average will increase by this amount when the SAT mathematics score does not change.
If the variable x1 is held constant, then only changes in x2 will impact the predicted values of ŷ. Since the coefficient of x2 is positive, for each one-unit increase of x2, the values of ŷ will increase by the value of ?2, where
?2 = .
In context, for each one point increase of the SAT mathematics score, the final college grade point average will increase by this amount when the high-school grade point average does not change.
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