Chapter 12, Problem R12.2RE

To determine

To verify that the conditions for inference about the slope of the least square regression line are met in this context.

Explanation of Solution

In this context from the previous exercise, we have to verify the conditions for inference about the slope of the least square regression line are: Linear, Independent, Normal, Equal standard deviation and Random.

Linear: it is satisfied because there is no strong curvature present in the residual plot.

Independent: It is satisfied because the sample of $36$ students at the high school is less than $10\%$ of all students at the high school.

Normal: It is satisfied because the highest bars in the histogram, are roughly in the middle of the histogram and thus the residual have approximately a normal distribution.

Equal standard deviation: It is satisfied because the vertical spread in the points of the residual plot is roughly the same everywhere in the graph.

Random: It is satisfied because the sample is a random sample.

Thus, since all conditions are satisfied it is appropriate to perform about the regression line.