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

Which of the following would have resulted in a violation of the conditions for inference?

a. If the entire sample was selected from one classroom

b. If the sample size was $15$instead of $25$

c. If the scatterplot of $x=footlength\&y=height$did not show a perfect linear relationship

d. If the histogram of heights had an outlier

e. If the standard deviation of foot length was different from the standard deviation of height

Short answer

The correct option is option (a)If the entire sample was selected from one classroom

Step-by-step solution

Given Information 

Given in the question that

we have to determine the correct option

Explanation 

Inference requirements for regression: linear, same standard deviation "Independent," "normal," and "random" are all phrases that are used interchangeably.

The violation is due to the fact that the sample must be random.

b. Because there is no sample size restriction, there is no violation.

c. Because there must be a linear relationship (Linear condition) between $x\&y$and, there is no violation. A perfect line relationship, on the other hand, is not essential.

d. There is no violation because the $y$-variable's distribution is unconstrained.

g. Because the Equal standard deviation requirement demands that the vertical spread of the residuals be equal, there is no violation. In the residual figure, the standard deviation of the residuals (rather than the standard deviation of the sample) is the same everywhere.