Asked by Nicole Salazar on Apr 30, 2024

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If all the points for a multiple regression model with two independent variables were right on the regression plane,then the coefficient of determination would equal:

A) 0.
B) 1.
C) 2,since there are two independent variables.
D) None of these choices.

Coefficient of Determination

A statistical measure that calculates the proportion of variance in the dependent variable predictable from the independent variable(s).

Regression Plane

A three-dimensional plane that best fits a set of points in a multiple regression model, used for prediction.

Independent Variables

Variables in an experiment or statistical model that are manipulated or changed to determine their effects on dependent variables.

  • Master the concept and significance of the coefficient of determination in the realm of multiple regression.
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riley williamsMay 06, 2024
Final Answer :
B
Explanation :
If all the points for a multiple regression model with two independent variables were right on the regression plane, that means there is no error or residual term present. In such a case, the SST (total sum of squares) will be equal to the SSR (regression sum of squares), since there will be no SSE (error sum of squares). Hence, R-squared will be equal to SSR/SST, which will be equal to 1 as all the points will perfectly fit the regression plane. Therefore, the answer is B.