Question

Calculating and interpreting residualsYou might need: CalculatorJoe sells used cars. He recorded the age (in years) of each car on his lot along with the number of kilometers ithad been driven. After plotting his results, Joe noticed that the relationship between the two variables was fairlylinear, so he used the data to calculate the following least squares regression equation for predicting distancedriven from the age of the car:♡ = 11,000+ 18,000What is the residual of a car that is 2 years old and has been driven 50,000 km?kmShow CalculatorStuck? Watch a video or use a hintReport a rable4 of 4

Answer 1

3000 km

Step-by-step explanation

The residual is the difference between the actual value of a data and the value that is predicted by the least square regression equation.

Residual = Actual Value - Predicted value

The least square regression equation for the given data is:

y = 11000 + 18000x

where x = age of the car

y = distance driven in the car

The actual value of the distance traveled given to us for a car that is 2 years old is 50000 km.

To get the predicted value, x will become 2 years, since we want to predict how far the car would have gone in 2 years. So:

y = 11000 + 18000(2)

y = 11000 + 36000

y = 47000

Therfore, the residual will be:

R = 50000 - 47000

R = 3000 km

That is the residual.