Question

Which of the following is not one of the conditions that must be satisfied in order to perform inference about the slope of a least-squares regression line? (a) For each value of x, the population of y-values is Normally distributed.

(b) The standard deviation $\sigma$of the population of y-values corresponding to a particular value of x is always the same, regardless of the specific value of x. (c) The sample size—that is, the number of paired observations (x, y)—exceeds $30$.

(d) There exists a straight line $y=\alpha +\beta x$such that, for each value of x, the mean ${\mu }_y$of the corresponding population of y-values lies on that straight line.

(e) The data come from a random sample or a randomized experiment.

Short answer

The condition that is satisfied in order to perform inference about the slope of a least-squares regression line is option (c) The sample size—that is, the number of paired observations (x, y)—exceeds$30$.

Step-by-step solution

Concept introduction

A regression line is marked in statistics that best govern the relationship of a set of data. In other phrases, it's a line that best describes a data set's trend.

Explanation

Random, Normal, Independent, Linear, and Equal variance are the five requirements for inferring the slope of a least-squares regression line.

(a) Must be met because it is a standard requirement.

(b) Must be satisfied because it is a criterion for equal variance.

(c) Must not be satisfied because there is no sample size constraint.

(d) This condition must be met because it is a Linear requirement.

Because it is a Random criterion, it must be satisfied.