Chapter 13, Section 13.1, Problem 020be with age. The research department at the

Question

Chapter 13, Section 13.1, Problem 020be with age. The research department at the company took a sample of An auto manufacturing company wanted to investigate how the price of one of its car models depreciates 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 3 2 4 2 2 5 2 4 Price 66 88 70 75 75 54 85 67 Find the least squares regression line equation in the form y a + br. use-Age" as the independent variable and-Price, as the dependent variable. Round your answers to four decimal places. +0 hr dy Predict the price of a 7 year-old car of this model Round your answer to one decimal place

Explanation / Answer

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Solving by hand, we calculate:
xbar = Sum( xi ) /n= 24 / 8 = 3
ybar = Sum( yi ) /n = 580 / 8 = 72.5
n = 8
Sxx = Sum( xi - xbar )^2 = 10
Sxy = Sum( xi - xbar )(yi - ybar) = -78
Syy = Sum( yi - ybar )^2 = 830

b1 = Sxy/Sxx = -7.8 and b0 = ybar - b1 * xbar = 95.9
Thus b1 = -7.8 and b0 = 95.9

Regression equation:
yhat = b0 + b1x = 95.9 -7.8x

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