Question

Do taller students require fewer steps to walk a fixed distance? The scatterplot shows the relationship between x=height (in inches) and y=number of steps required to walk the length of a school hallway for a random sample of 36 students at a high school.

A least-squares regression analysis was performed on the data. Here is some computer output from the analysis

Short answer

As a result, because all conditions have been met, it is okay to proceed with the regression line.

Step-by-step solution

Given information

The given data is

Explanation

We must validate the following assumptions for inference about the slope of the least square regression line in this context from the previous exercise: Linear, Independent, Normal, Equal standard deviation, and Random.

Because there is no significant curvature in the residual plot, it is satisfied.

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

Normal: The tallest bars in the histogram are about in the middle of the histogram, indicating that the residual has a normal distribution.

Because the vertical spread in the points of the residual plot is about the same everywhere in the plot, it is satisfied.

Because the sample is a random sample, it is satisfied.

As a result, because all conditions have been met, it is okay to proceed with the regression line.