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
A residual plot shows “Percent of high school graduates taking the SAT” along the horizontal axis ranging from 0 to 90 in increments of 10 and “Residual” along the vertical axis ranging from negative 50 to 50 in increments of 25. A horizontal line is drawn at 0 on the vertical axis across the graph. Dots are scattered on the either side of the line across the graph and between negative 30 and 35 on the vertical axis. A dot is shown before 20 on the horizontal axis between negative 70 on the vertical axis.
Explain how the residual plot shows that the Linear condition for performing inference about the slope is, or is not, met.

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

There is clear curvature in the residual plot, which confirms that the relationship between mean SAT score and percent taking is linear.

There is clear curvature in the residual plot, which suggests that the relationship between mean SAT score and percent taking is not linear.

There is clear curvature in the residual plot, which suggests 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, which confirms that the relationship between mean SAT score and percent taking is linear.