Question

the bureau of labor statistics is an office within the us department of labor. every three months the bureau releases a report containing jobs and salary data of us workers. one statistic reported is the median weekly salary for full - time workers. the scatterplot shows the growth of median weekly salary, starting in january 2010. an equation of the least - squares for the data in the scatterplot is \\( \overline{median salary}=17.327(year)-729.327 \\), where 2010 represents year zero. the value of \\( r \\) for the scatterplot is 0.977. based on the least - squares regression and residual plot, is a linear model suitable for this data set? a linear model is suitable because the value of \\( r \\) is close to 1. a linear model is suitable because the residual plot shows a curved pattern. a linear model is not suitable because the residual plot shows a clear pattern. a linear model is not suitable because there are more positive residuals than negative residuals.

Explanation:

To determine if a linear model is suitable, we check the residual plot. A linear model is appropriate when the residual plot has no clear pattern (random scatter). If there is a clear pattern (like a curve), the linear model is not suitable. The value of \( r \) (correlation coefficient) close to 1 only indicates a strong linear relationship but doesn't confirm the model's suitability if the residual plot has a pattern. The number of positive and negative residuals (as long as they are randomly distributed) doesn't affect model suitability.

Answer:

A linear model is not suitable because the residual plot shows a clear pattern.