Question

Question 6 View Policies Current Attempt in Progress 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 2 7 8 5 6 3 4 7 Price 87 27 28 59 53 66 53 39 Find the least squares regression line equation in the form 9 = a + bx. Use "Age as the independent variable and "Price" as the dependent variable. Round your answers to four decimal places. ya Predict the price of a 3 year-old car of this model Round your answer to one decimal place. pred

Answer 1

The statistical software output for this problem is:

Simple linear regression results: Dependent Variable: Price Independent Variable: Age Price = 98.166667-8.8888889 Age Sample size: 8 R (correlation coefficient) = -0.936146 R-sq = 0.87636933 Estimate of error standard deviation: 7.6497398 Parameter estimates: Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 98.166667 7.6497398 0 6 12.832681 <0.0001 Slope -8.8888889 1.362986 0 6 -6.5216291 0.0006

Hence,

a) Regression equation is:

$\small \widehat{y}$ = 98.1667 + (-8.8889) x

b) Predicted price = 98.1667 - 8.8889*3 = 71.5