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Subject Test Math 1

Question 32 of 32

beginning of content:
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SAT Subject Test

Time t

(years)

0 1 2 5

Value v(t)

(dollars)

15,000 13,000 10,900 3,000

When purchased, an automobile is valued at $ 15 , 000. 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 t equals 4 invisible times?

Select an Answer

$ 5 comma 400

Correct Answer: 
No

$ 5 comma 500

Correct Answer: 
No

$ 5 comma 600

Correct Answer: 
Yes

$ 6 comma 400

Correct Answer: 
No

$ 7 comma 000

Correct Answer: 
No

The correct answer is C.

To determine the value, to the nearest hundred dollars, of the automobile when t equals 4, find the equation of the least-squares regression line and then evaluate that equation at t equals 4 invisible times.

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, 15 , 332 for the y-intercept and negative 2 , 429 for the slope, so the regression line is given by the equation y equals negative 2 , 429 t plus 15 , 332. When t equals 4 invisible times, one gets y equals negative 2 , 429 left parenthesis 4 right parenthesis plus 15 , 332 equals 5 , 616. Therefore, based on the least-squares linear regression, the value, to the nearest hundred dollars, of the automobile when t equals 4 invisible times is $ 5 , 600.

Question Difficulty: 
hard