A used car dealer wants to develop a regression equation that determines mileage

Question

A used car dealer wants to develop a regression equation that determines mileage as a function of the age of a car in years. He collects the data shown below for the 12 cars he has on his lot. a) What is the slope of the regression equation? Give your answer to two decimal places. b) What is the value of the correlation coefficient? Give your answer to two decimal places. c) A 4 year old car is delivered to his lot with 160000 miles. Manually enter these values in the data table above and rerun the regression analysis. What is the value of the slope? Give your answer to two decimal places. d) Including the additional car, what is the value of the correlation coefficient? Give your answer to two decimal places. e) Did the additional car strengthen or weaken the linear relationship between age and mileage? Can not be determined. It strengthened the linear relationship. It weakened the line relationship.

Explanation / Answer

a) Slope of coefficient of equation is 11008.13 using Data Analysis option and selecting Regression in Excel

b) Correlation Coefficient is 0.97558 using correl function in R. Also for single independent variable square root of R square gives the value of correlation coefficient

c) After re run the slope coefficient is 7460.65

d) Correlation Coefficent is 0.64 after including additional data point

e) Additional data point weaken the relationship as the R square is dropped to 0.40 from 0.95

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