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, $x=footlength\&y=height$ere 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:

26. Which of the following is the best interpretation of the value $0.4117$in the computer output?

a. For each increase of $1cm$in foot length, the average height increases by about$0.4117cm$

b. When using this model to predict height, the predictions will typically be off by about $0.4117cm$.

c. The linear relationship between foot length and height accounts for $41.17\%$of the variation in height.

d. The linear relationship between foot length and height is moderate and positive.

e. In repeated samples of size $25$the slope of the sample regression line for predicting height from foot length will typically vary from the population slope by about $0.4117$.

Short answer

The correct option is option (e)

In repeated samples of size$25$the slope of the sample regression line for predicting height from foot length will typically vary from the population slope by about $0.4117$

Step-by-step solution

Given Information

Given in the question that

we have to determine the correct option.

Explanation 

The number $0.4117$is mentioned in the column "SE Coef" and in the row "foot length," indicating that $0.4117$is the standard error of the slope $SE{b}_1$

The average deviation of the slope of the sample regression line from the population regression line is shown by the standard error of the slope.

As a result, the best solution is (e)