Question

A researcher at a large company has collected data on the beginning salary and current salary of 48 randomly selected employees.
The least‑squares regression equation for predicting their current salary from their beginning salary is $\hat y$ = - 2532.7 + 2.12 x.
Mrs. Kathy Jones started working for the company earning $19,000. She currently earns $40,000. What is the residual for Ms. Jones?

Answer 1

Answer:

$2252.7

Explanation:

Residual is calculated by taking the difference of observed and predicted value.

The regression equation is

y= - 2532.7 + 2.12 x.

Where, y is the current salary and x is the beginning salary.

Mrs. Kathy Jones beginning salary= $19,000.

Mrs. Kathy Jones observed current salary= $40,000.

Residual for Mrs. Kathy Jones=Mrs. Kathy Jones observed current salary-Mrs. Kathy Jones predicted current salary.

Mrs. Kathy Jones predicted current salary

y^=  - 2532.7 + 2.12 (19000)

y^=  - 2532.7 + 40280

y^=37747.3

Mrs. Kathy Jones predicted current salary =$37,747.3

Residual for Mrs. Kathy Jones= $40,000-$37,747.3

Residual for Mrs. Kathy Jones=$2252.7

The residual for Mrs. Kathy Jones is $2252.7.