1. 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 (x) 8 3 6 9 2 5 6 3
Price (y) 16 74 40 19 124 36 33 89
a) Find the value of the linear correlation coefficient r.
b) Find the value of the coefficient of determination r2, and interpret the meaning for this problem.
c) At the 0.05 level of significance, is there a significant linear relationship between two variables?
d) Determine the adequacy of the fit of the model.
e) Evaluate whether the assumptions of regression have been seriously violated.
f) If there is a linear correlation, what is the regression equation?
g) Interpret the meaning of the slope b1 in this problem.
h) Interpret the meaning of the Y-intercept b0 in this problem. Will it make sense to you as far as this model is concerned? Explain why.
i) Set up a 95% confidence interval estimate of the population slope.
j) Set up a 95% confidence interval estimate of the average price for all cars of this model after 7 years.
k) Set up a 95% confidence interval of the average price of a car of this model after 7 years.
l) Explain the difference in the results obtained in (j) and (k).
The solution provides step by step method for the calculation of correlation coefficient, coefficient of determination, test statistic for significance of correlation coefficient and regression analysis. Formula for the calculation and Interpretations of the results are also included.