Question

From 1975 to 1986, the General Social Survey asked its participants if they favored or opposed capital punishment. A least squares regression line was calculated to predict the percent that favored the death penalty based on the year. The least squares regression equation is yhat= -1912.49+1.003x. Interpret the y-intercept for this equation, if appropriate.

Answer 1

The y-intercept is not appropriate.

Explanation:

The given expression is

`y=-1912.49+1.003x`

This linear regression expresses a line in its explicit form

`y=mx+b`

Where
`b=-1912.49` represents the y-interception.

This element of the linear regression represents the initial condition of the modelled problem, that is, in this case is the initial year.

So, it doesn't make sense that the initial year is -1912.49, because years are whole number, they are not represented as decimals. Additionally, years cannot be negative numbers, because it won't make sense, time cannot go backwards.

Therefore, the y-interception is not appropriate to model this problem.

Answer 2

The y-intercept for this equation makes no sense for this model.

Explanation:

In this case, the explanatory variable x is the year when the observations were taken. So, the values are the integer numbers between (and including) 1975 and 1986.

The y-intercept for the equation of the linear regression makes no sense for this prediction, for it would correspond to the value x=0 (the year 0) is not consider in the range of the explanatory data.