Question

SAT Math scores Is there a relationship between the percent of high school graduates in each state who took the SAT and the state’s mean SAT Math score? Here is a residual plot from a linear regression analysis that used data from all $50$states in a recent year. Explain why the conditions for performing inference about the slope $\beta 1$ of the population regression line are not met.

Short answer

The relationship between mean SAT score and percent taking is linear.

Step-by-step solution

Given information:

We have been given that:

Residual plot from a linear regression analysis that used data from all$50$ states in a recent year

Explanation:

A residual plot shows "Percent of high school graduates taking the SAT" along the horizontal axis in increments of $10$and "Residual" along the vertical axis in increments of $25$. Horizontal line is drawn at $0$on vertical axis across the graph. Dots are scattered across the graph on either side of the line and on the vertical axis between negative $30$and $35$. A dot is shown before $20$on the horizontal axis and between negative $70$on the vertical axis.

Explain how the residual plot indicates whether or not the Linear condition for performing slope inference is met.

The variability of the residuals in the vertical direction is roughly the same from the smallest to the largest -value, indicating that the relationship between mean SAT score and percent taking is not linear.

The residual plot shows a clear curvature, confirming that the relationship between mean SAT score and percent taking is linear.

The residual plot has significant curvature, indicating that the relationship between mean SAT score and percent taking is not linear.

The residual plot has significant curvature, indicating that the relationship between mean SAT score and residual values is not linear.

The variability of the residuals in the vertical direction is roughly the same from the smallest to the largest -value, confirming that the relationship between mean SAT score and percent taking is linear.