Question

A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects 6 months of data consisting of monthly tire sales (in thousands of tires) and monthly advertising expenditures (in thousands of dollars). The simple linear regression equation is ŷ = 3 + 1x. The dealer randomly selects one of the six observations, with a monthly sales value of 8,000 tires and monthly advertising expenditures of $7,000. Calculate the value of the residual for this observation. Explain how to get the answer please.

Answer 1

Residual = Actual value - Predicted value

Here actual value is given as $7000.

For 8000 tires, x value will be 8 as x is in thousand of tires. Hence,

y = 3 + 1*8 = 11 (In thousand of dollars)

Hence,

Predicted value = $11000

Therefore,

Residual = 7000 - 11000 = - 4000