A linear regression model based on a random sample of 36 observations on the response variable and 4 predictors has a multiple coefficient of determination equal to 0.697. What is the value of the adjusted multiple coefficient of determination? Answer:
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697 \) (given) - \( n = 36 \) (number of observations) - \( k = 4 \) (number of predictors) Show more…
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A linear regression model based on a random sample of 36 observations on the response variable and 4 predictors has a multiple coefficient of determination equal to 0.697. What is the value of the adjusted multiple coefficient of determination?
Pritesh R.
The following estimated regression equation was developed for a model involving two independent variables. $$\hat{y}=40.7+8.63 x_{1}+2.71 x_{2}$$ $$\begin{array}{c}{\text { After } x_{2} \text { was dropped from the model, the least squares method was used to obtain an }} \\ {\text { estimated regression equation involving only } x_{1} \text { as an independent variable. }} \\ {\hat{y}=42.0+9.01 x_{1}}\end{array}$$ \begin{equation} \begin{array}{l}{\text { a. Give an interpretation of the coefficient of } x_{1} \text { in both models. }} \\ {\text { b. } \text { Could multicollinearity explain why the coefficient of } x_{1} \text { differs in the two models? If }} \\ {\text { so, how? }}\end{array} \end{equation}
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