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.

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 two models is superior for prediction purposes.

Answer 1

To determine which prediction is better, we need to compare the coefficients of determination (R-squared) for both models. If Model 1 has a higher R-squared value than Model 2, then a prediction based on Model 1 is better. If Model 2 has a higher R-squared value, then a prediction based on Model 2 is better. If the R-squared values are the same, there is no difference in predictive ability.

Step-by-step explanation:

The question presents the results of two separate simple linear regression models based on the same set of observations on a specified dependent variable. To determine which prediction is better, we need to compare the coefficients of determination (R-squared) for both models. The coefficient of determination measures the proportion of the variance in the dependent variable that can be explained by the independent variable. If Model 1 has a higher R-squared value than Model 2, then we can conclude that a prediction based on Model 1 is better than a prediction based on Model 2. Conversely, if Model 2 has a higher R-squared value, then a prediction based on Model 2 is better than a prediction based on Model 1. If the R-squared values are the same for both models, then there is no difference in the predictive ability between the two models.

Answer 2

A. A prediction based on Model 1 is better than a prediction based on Model 2.

Step-by-step explanation:

Given :

Model 1 :

R² = 0.92

s = 1.65

Model 2 :

R² = 0.85

s = 1.91

The Coefficient of determination of the first model is 0.92 which is greater than the coefficient of determination of the Second model, the coefficient of determination gives the proportion of variation in the dependent variable which is caused by the regression line. Hence, we can say a prediction based on Model 1 is better than a prediction based on Model 2 because a larger proportion of the variation in the dependent variable is predictable from the independent variable.