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Q. 1

Expert-verifiedFound in: Page 796

Book edition
4th

Author(s)
David Moore,Daren Starnes,Dan Yates

Pages
809 pages

ISBN
9781319113339

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.

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 $30$.

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.

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.

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