Solution — 2017 Question 9 Regression

Using GC, $$r=0.978∎$$

This indicates a strong positive linear correlation between the number of years of service and the weekly earnings of production line employees.

Using GC, the equation of the regression line of $y$ on $x$ is $$y=0.182x+2.56∎$$

When $x=2,$

The estimated weekly earnings for an employee with $2$ years of service is $\$293∎$

Two reasons why Sue’s conclusion might not be justified:

1. $x=2$ lies outside the data range $11\le x\le 40$ (extrapolation), so the estimate may be unreliable $∎$
2. Individual earnings may be influenced by factors other than years of service, such as performance, job role or negotiated salary, so the regression line may not apply to Sue’s situation $∎$