For the same set of observations on a specified dependent variable,two different independent variables were used to develop two separate simple linear regression models.A portion of the results is presented below. $$\begin{array}{l}
\text { Model 1 } \quad \text { Model 2 } \
{ r ^ { 2 } = .92 }\quad { r ^ { 2 } = .85 }\
s = 1.65 \quad s = 1.91
\end{array}$$

Based on the results given above,we can conclude that:
A)A prediction based on Model 1 is better than a prediction based on Model 2.
B)A prediction based on Model 2 is better than a prediction based on Model 1.
C)There is no difference in the predictive ability between Model 1 and Model 2.
D)There is not sufficient information to determine which of the two models is superior for prediction purposes.

Question

For the same set of observations on a specified dependent variable,two different independent variables were used to develop two separate simple linear regression models.A portion of the results is presented below. $$\begin{array}{l}
 \text { Model 1 } \quad \text { Model 2 } \
{ r ^ { 2 } = .92 }\quad { r ^ { 2 } = .85 }\
s = 1.65 \quad s = 1.91
\end{array}$$

Based on the results given above,we can conclude that:
A)A prediction based on Model 1 is better than a prediction based on Model 2.
B)A prediction based on Model 2 is better than a prediction based on Model 1.
C)There is no difference in the predictive ability between Model 1 and Model 2.
D)There is not sufficient information to determine which of the two models is superior for prediction purposes.

Quizplus · Accepted Answer

The coefficient of determination ($r^2$) measures the proportion of the variation in the dependent variable that can be explained by the independent variable in the regression model. Therefore, the higher $r^2$, the better the model fits the data.

In this case, Model 1 has a higher $r^2$ value, which indicates that it explains more of the variability in the dependent variable than Model 2. Additionally, Model 1 has a smaller value of residual standard error ($s$) than Model 2, which suggests that the data points are closer to the fitted regression line in Model 1.

Therefore, we can conclude that Model 1 is better suited for prediction purposes than Model 2.

For the Same Set of Observations on a Specified Dependent Model 1 Model 2 r2=.92r2=.85s=1.65s=1.91\begin{array}{l} \text { Model 1 } \quad \text { Model 2 } \\{ r ^ { 2 } = .92 }\quad { r ^ { 2 } = .85 }\\s = 1.65 \quad s = 1.91\end{array} Model 1 Model 2 r2=.92r2=.85s=1.65s=1.91​

For the Same Set of Observations on a Specified Dependent $\begin{array}{l} \text { Model 1 } \quad \text { Model 2 } \\{ r ^ { 2 } = .92 }\quad { r ^ { 2 } = .85 }\\s = 1.65 \quad s = 1.91\end{array}$