Joe’s mom says that he’ll have to pay outrageous insurance rates on a Porsche. Joe has been told that insurance rates are dependent upon the driver’s age.   His driver’s training instructor gave Joe the following table to help him out. It shows insurance rates for a male Porsche driver with a perfect driving record based on different ages.   Find the equation of the model of best fit 

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Expert Answers

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Given the values in the table we can compute the line of best fit.

Note that when the points given are plotted, they appear to lie along a line with a negative slope. (As the insurance buyer ages, the rates go down.)

Using an algebra utility (a graphing calculator or spreadsheet) we find the equation of the line of best fit to be `hat(y)=-252.12x+10091.51 ` where `hat(y) ` represents the charge for a given age x.

(Note that in real life this is certainly an approximation -- age is continuous but the rates will probably only change annually.)

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The line of best fit is `hat(y)=-252.12x+10091.51 `

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The slope is negative as the rates decrease with advancing age. There is almost certainly a domain restriction (must be at least 16 to drive, whole numbers of years, and the rate probably rises again with advanced age.)

The r value is -.999299 indicating a very strong, negative linear association.

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