Question

2.2. Refer to Exercise 11.76 where we obtained the following information when fitting a multiple regression model to 15 responses; $$\hat{y}=38.83-0.0092 x_{1}-0.92 x_{2}+11.56 x_{3}, \quad S_{y y}=10965.46, \quad \mathrm{SSE}=1107.01$$. a. Is there sufficient evidence to conclude that at least one of the independent variables contributes significant information for the prediction of $Y ?$ b. Calculate the value of the multiple coefficient of determination. Interpret the value of $R^{2}$.

          2.2. Refer to Exercise 11.76 where we obtained the following information when fitting a multiple regression model to 15 responses; $$\hat{y}=38.83-0.0092 x_{1}-0.92 x_{2}+11.56 x_{3}, \quad S_{y y}=10965.46, \quad \mathrm{SSE}=1107.01$$. 
a. Is there sufficient evidence to conclude that at least one of the independent variables contributes significant information for the prediction of $Y ?$
b. Calculate the value of the multiple coefficient of determination. Interpret the value of $R^{2}$.

Added by Rodrigo G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

07/04/2023

Step 1

To determine if there is sufficient evidence to conclude that at least one of the independent variables contributes significant information for the prediction of $Y$, we can perform an F-test. The F-test statistic is given by: $$F = \frac{SSR / (k - 1)}{SSE / (n Show more…

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2.2. Refer to Exercise 11.76 where we obtained the following information when fitting a multiple regression model to 15 responses; $$\hat{y}=38.83-0.0092 x_{1}-0.92 x_{2}+11.56 x_{3}, \quad S_{y y}=10965.46, \quad \mathrm{SSE}=1107.01$$. a. Is there sufficient evidence to conclude that at least one of the independent variables contributes significant information for the prediction of $Y ?$ b. Calculate the value of the multiple coefficient of determination. Interpret the value of $R^{2}$.