I. A random sample of ten used cars (Corvettes) between 1 and 6 years old were selected from a used car dealership. The following data were obtained. x represents age, in years, and y represents sales price, in hundreds of dollars.
x 6 6 6 4 2 5 4 5 1 2
y 125 115 130 160 219 150 190 163 260 260
1. Graph the data in a scatterplot to determine whether there is a possible linear relationship between the two variables. Draw the proposed model in the scatter diagram.
2. Fit a linear model to the data.
3. Write the least squares equation.
4. Interpret the regression coefficients in the context of the problem.
5. What is the value of the correlation coefficient? What does it mean in terms of the strength and nature of the relationship between the two variables?
6. Compute and interpret the coefficient of determination. Interpret its meaning.
7. Based on the coefficient of determination and the standard error of estimate, how good is the model?