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# Use the following to answer the questions below:Data were collected on the age (in years), mileage ...

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Use the following to answer the questions below:

Data were collected on the age (in years), mileage (in thousands of miles), and price (in thousands of dollars) of a random sample of used Hyundai Elantras. Output from two models are provided.

Single Predictor Model:
The regression equation is Price = 13.8 - 0.0912 Mileage

 Predictor Coef SE Coef T P Constant 13.7751 0.6930 19.88 0.000 Mileage -0.091167 0.009718 -9.38 0.000

Two Predictor Model:
The regression equation is Price = 15.2 - 0.0101 Mileage - 1.55 Age

 Predictor Coef SE Coef T P Constant 15.2174 0.6112 24.90 0.000 Mileage -0.01005 0.01977 -0.51 0.616 Age -1.5466 0.3508 -4.41 0.000

S = 1.39445       R-Sq = 89.0%        R-Sq(adj) = 88.0%

Analysis of Variance

 Source DF SS MS F P Regression 2 346.11 173.06 89.00 0.000 Residual Error 22 42.78 1.94 ​ ​ Total 24 388.89 ​ ​ ​

Regression output for the model that only uses Age as a predictor in the model is provided. Assuming that the residuals for this single predictor model do not indicate any problems, is this model an improvement over the model that uses both Age and Mileage as predictors?  Statistically justify your answer by discussing at least two quantitative criteria.

The regression equation is Price = 15.3 - 1.71 Age

 Predictor Coef SE Coef T P Constant 15.2912 0.5840 26.18 0.000 Age -1.7126 0.1264 -13.55 0.000
S = 1.37179        R-Sq = 88.9%        R-Sq(adj) = 88.4%

Analysis of Variance

 Source DF SS MS F P Regression 1 345.61 345.61 183.66 0.000 Residual Error 23 43.28 1.88 ​ ​ Total 24 388.89 ​ ​ ​
Textbook

## Statistics: Unlocking the Power of Data

Edition: 3rd
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mkql12mkql12
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