Question

Multiple Choice Select the best answer for Exercises 23-28. Exercises 23-28 refer to the following setting. To see if students with longer feet tend to be taller, a random sample of $25$students was selected from a large high school. For each student,$x=footlength$and$y=height$were recorded. We checked that the conditions for inference about the slope of the population regression line are met. Here is a portion of the computer output from a least-squares regression analysis using these data:

The slope ${\beta }_1$of the population regression line describes

a. the exact increase in height (cm) for students at this high school when foot length increases by$1$.

b. the average increase in foot length(cm) for students at this high school when height increases by $1$.

c. the average increase in height (cm) for students at this high school when foot length increases by$1$.

d. the average increase in foot length (cm) for students in the sample when height increases by$1$

e. the average increase in height(cm) for students in the sample when foot length increases by$1$

Short answer

The correct option is option (c)

The average increase in height (cm) for students at this high school when foot length increases by$1$

Step-by-step solution

Given Information

Given in the question that

We have to determine the correct option.

Explanation

$x=footlegth$

$y=height$

${\beta }_1=$slope of the population regression line.

The average of $y$in the population per unit of $x$is shown by the slope of the population regression line.

As a result, ${\beta }_1$depicts the average increase in height of the entire population per cm of foot length.

so, the correct option is option (c)