When purchased, an automobile is valued at Its value depreciates at the rate shown in the table above. Based on a least-squares linear regression, what is the value, to the nearest hundred dollars, of the automobile when ?
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The correct answer is C.
To determine the value, to the nearest hundred dollars, of the automobile when , find the equation of the least-squares regression line and then evaluate that equation at .
A calculator can be used to find the least-squares regression line. The specific steps to be followed depend on the model of calculator, but they can be summarized as follows. Enter the statistics mode, edit the list of ordered pairs to include only the four points given in the table, and perform the linear regression. The coefficients will be, approximately, for the -intercept and for the slope, so the regression line is given by the equation . When , one gets . Therefore, based on the least-squares linear regression, the value, to the nearest hundred dollars, of the automobile when is .