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Chapter 12: Q. 3 (page 796)

Inference about the slope βof a least-squares regression line is based on which of the following distributions?

(a) The t distribution with n-1degrees of freedom

(b) The standard Normal distribution

(c) The chi-square distribution with n-1degrees of freedom

(d) The t distribution with n-2degrees of freedom

(e) The Normal distribution with mean μand standard deviationσ

Short Answer

Expert verified

Inference about the slope βof a least-squares regression line is based on option (d) The tdistribution with n-2degrees of freedom.

Step by step solution

01

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.

02

Explanation

We must estimate two parameters (the y-intercept αand the slope β) in order to find the least-squares regression line.

The t-distribution with degrees of freedom equal to the sample size nminus the number of calculated parameters becomes the appropriate distribution.

df=n-2.

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Most popular questions from this chapter

Do hummingbirds prefer store-bought food made from concentrate or a simple mixture of sugar and water? To find out, a researcher obtains 10identical hummingbird feeders and fills 5, chosen at random, with store-bought food from concentrate and the other 5with a mixture of sugar and water. The feeders are then randomly assigned to10possible hanging locations in the researcher’s yard. Which inference procedure should you use to test whether hummingbirds show a preference for store-bought food based on amount consumed?

(a) A one-sample z test for a proportion .

(b) A two-sample z test for a proportion .

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(e) A paired t test .

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