Chapter 4, Problem 1CR

Terminology Consider the equation of a least-squares line $\stackrel{\wedge }{y}=3+2x$ based on data pairs (x, y). Which variable is the explanatory variable, and which is the response variable?

To determine

The explanatory variable and the response variable.

Answer to Problem 1CR

Solution: The explanatory variable is x and the response variable is y.

Explanation of Solution

Given: The least-squares line, $\widehat{y}=3+2x$ is given in the question.

Calculation: The general equation for the least-squares line is,

$\widehat{y}=a+bx$

Here, a represents the y-intercept and b represents the slope of the line.

The explanatory variable is an independent variable, which is used to predict another variable. In the provided least-squares line, the explanatory variable is denoted by x.

The response variable is a dependent variable, which is being predicted. In the provided least-squares line, the response variable is denoted by y.

Therefore, the explanatory and response variables are x and y, respectively.