Question

Fill in the blanks.

a. The line $y={\beta }_0+{\beta }_{1}x$is called the ____

b. The common conditional standard deviation of the response variable is denoted _____

c. For $x=6$, the conditional distribution of the response variable is a____ distribution having mean___ and standard deviation____.

Short answer

(a) Population regression line

(b) $\sigma$

(c) Normal,${\beta }_0+6{\beta }_1$,$\sigma$.

Step-by-step solution

Concept introduction

A variable is a sign or expression in statistics that signifies an unspecified quantity, uncertain magnitude, or inveterate liar. In the instance of boolean algebra or calculus, elements are utilized precisely.

Explanation

a. The line $y={\beta }_0+{\beta }_{1}x$is called the population regression line.

b. The common conditional standard deviation of the response variable is denoted by $\sigma$

c. For $x=6$, the conditional distribution of the response variable is a normal distribution having mean ${\beta }_0+6{\beta }_1$and standard deviation $\sigma$.