Question

An auto manufacturing company wanted to investigate how the price of one of its car models depreciates with age. The research department at the company took a sample of eight cars of this model and collected the following information on the ages (in years) and prices (in hundreds of dollars) of these cars.

Age	4	4	7	7	4	6	8	2
Price	64	70	40	39	63	45	20	82

Find the least squares regression line equation in the form y^=a+bx. Use "Age" as the independent variable and "Price" as the dependent variable.

Round your answers to four decimal places.

y^=

Predict the price of a 8 year-old car of this model.

Round your answer to one decimal place.

ypred=

Answer 1

Sum of X = 42
Sum of Y = 423
Mean X = 5.25
Mean Y = 52.875
Sum of squares (SS_X) = 29.5
Sum of products (SP) = -285.75

Regression Equation = ŷ = bX + a

b = SP/SS_X = -285.75/29.5 = -9.6864

a = M_Y - bM_X = 52.88 - (-9.69*5.25) = 103.7288

ŷ = -9.6864X + 103.7288

For x=8, ŷ = (-9.6864*8) + 103.7288=26.2376=26.2