Question

In a residual plot against x that does NOT suggest we should challenge the assumptions of our regression model, we would expect to see a _____. a. parabolic band of points b. band of points having a slope consistent with that of the regression equation c. horizontal band of points centered near 0 d. widening band of points

Answer 1

In a residual plot against x that does NOT suggest we should challenge the assumptions of our regression model, we would expect to see a c. horizontal band of points centered near 0.

Step-by-step explanation:

In the context of regression analysis, a residual plot helps us assess the fit of a regression model. When analyzing a residual plot against the independent variable x, a pattern that does NOT suggest we should challenge our model's assumptions would be a c. horizontal band of points centered near 0. This indicates that the residuals are evenly spread around the regression line and do not show a systematic pattern. Such a distribution of points supports the idea that the regression line fits the data well, the error variance is constant (homoscedasticity), and the model assumptions are likely to be valid.

If we observe a parabolic or widening band of points, or a band with a slope, it would indicate that the assumptions of equal variance, linearity, and independence of errors might be violated.

Answer 2

In a residual plot against x that does NOT suggest we should challenge the assumptions of our regression model, we would expect to see a _____.

c. horizontal band of points centered near 0

Step-by-step explanation:

This residual graph or plot shows the residual values (or the difference between the observed y-value (from scatter plot) and the predicted y-value (from regression equation line) on the vertical axis and displays the independent variable on the horizontal axis. A linear regression model becomes appropriate for a dataset when the points are randomly dispersed around the horizontal axis near 0; otherwise, a nonlinear model becomes more appropriate.