SAT Math Multiple Choice Question 435: Answer and Explanation

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Question: 435

15. Use the data in the scatterplot and the line of best fit shown to answer the following question.

According to the graph, the data has been modeled using a line of best fit. Another researcher thinks that an exponential model may be a better fit. The table below shows the researcher's results after using a graphing calculator to perform a linear regression and an exponential regression on the data.

LinReg ExpReg
y = ax + b y = a × bx
a = 2.7 a = 1.251327
b = .68888889 b = 2.299749
r2 = .81876039 r2 = .84304281
r = .9048538 r = .9181736

Which of the following best explains which regression model is a better fit and why?

  • A. A linear model is a much better fit because its value of a is considerably higher.
  • B. A linear model is a slightly better fit because its value of r is slightly smaller.
  • C. An exponential model is a much better fit because its value of a is much closer to 1.
  • D. An exponential model is a slightly better fit because its value of r is slightly closer to 1.

Correct Answer: D

Explanation:

D

Difficulty: Medium

Category: Problem Solving and Data Analysis / Scatterplots

Strategic Advice: Performing a regression on a graphing calculator (or using computer software) tells you the approximate equation that could be used to model the data and how well the model fits the data. The fit is indicated by the correlation coefficient, r. The closer this number is to 1 (a 100% fit), the more accurately the model describes the data.

Getting to the Answer: You can eliminate A and C right away because they do not involve the correlation coefficient, r. To choose between B and (D), look at the value of r to find that 0.9181736 is slightly closer to 1 than 0.9048538. This means the exponential model is a slightly better fit than the linear model.

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