Question

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

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

(b) The standard Normal distribution

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

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

(e) The Normal distribution with mean $\mu$and standard deviation$\sigma$

Short answer

Inference about the slope $\beta$of a least-squares regression line is based on option (d) The $t$distribution with $n-2$degrees of freedom.

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

We must estimate two parameters (the $y$-intercept $\alpha$and the slope $\beta$) in order to find the least-squares regression line.

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

$df=n-2$.