Question

two different regression models were used to describe the relationship between two variables x and y, for a sample of 25 individuals. the equation of the least - squares regression lines are given for model 1 and model 2, in addition to the residual plot for each model. which model is more appropriate, and why? a) model 1 because x and y have a linear relationship. b) model 1 because approximately half of the residuals are positive, and approximately half of the residuals are negative. c) model 2 because x and y have a linear relationship. d) model 2 because x and ln y have a linear relationship. e) model 2 because the slope of the regression line is close to 1.

Explanation:

In regression analysis, if the relationship between $x$ and $\ln y$ is linear, a model based on this transformation is appropriate. A linear relationship between $x$ and $\ln y$ can be better - modeled by a regression line. The presence of a linear relationship between variables is a key factor in choosing a regression model. Option A and C assume a simple linear relationship between $x$ and $y$ without considering possible transformations. Option B's reasoning about the proportion of positive and negative residuals is not a sufficient reason for model - selection. Option E's focus on the slope being close to 1 is not the main criterion for model appropriateness.

Answer:

D. Model 2 because $x$ and $\ln y$ have a linear relationship.