Question

Two measures, x and y, were taken on 20 subjects. Two regressions were performed and resulted in the following residual plots.

Regression 1 → y hat equals negative 553.919 plus 2.93759 times x and r2 = 0.93.

Regression 2 → log of y hat = 1.32112 + 0.003827x and r2 = 0.98.

Which of the following conclusions is best supported by the evidence above?

Regression 1 is a better fit because there appears to be a linear relationship between x and y.
Regression 2 is a better fit because there appears to be a linear relationship between x and y.
Regression 1 is a better fit because there appears to be a nonlinear relationship between x and y.
Regression 2 is a better fit because there appears to be a nonlinear relationship between x and y.

Answer 1

Based on the regression line 2 is a better fit because it is non liner

Answer 2

Answer: Based on the information provided, the best conclusion supported by the evidence is:

Regression 2 is a better fit because there appears to be a linear relationship between x and y.

Step-by-step explanation:

1. Regression 1: The equation for regression 1 is y hat = -553.919 + 2.93759x, indicating a linear relationship between x and y. However, the residual plot is not given, so we cannot fully assess the goodness of fit for regression 1.

2. Regression 2: The equation for regression 2 is log(y hat) = 1.32112 + 0.003827x, which implies a linear relationship between x and the logarithm of y. The given information states that the residual plot is provided, but it doesn't mention any nonlinearity. Therefore, without additional information about the residual plot, we cannot determine whether there is a nonlinear relationship.

Given that regression 2 has a higher R-squared value of 0.98 compared to regression 1's R-squared value of 0.93, it suggests that regression 2 explains more of the variability in the data. However, without additional information about the residual plots, we cannot conclusively determine the presence of a nonlinear relationship. Therefore, the best-supported conclusion is that regression 2 is a better fit because there appears to be a linear relationship between x and y, as indicated by the given equation.

Step-by-step explanation: