# Correlation and regression - total variation

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Refer to the minitab display obtained by using the paired data consisting of weights (in lb) of 32 cars and their highway fuel consumption amounts (in mi/gal). Along with the paired sample data, minitab was also given a car weight of 4000 lb to be used for predicting the highway fuel consumption amount

The regression equation is

Highway = 50.5 - 0.00587 Weight

Predictor Coef SE Coef T P

Constant 50.502 2.86 17.66 0.000

Weight -0.0058685 0.0007859 -7.47 0.000

s= 2.19498 R-Sq = 65% R-Sq(adj) = 63.9%

Predicted Values for New Observations

New

Obs Fit SE Fit 95% CI 95% PI

1 27.028 0.497 (26.013, 28.042) (22.431, 31.624)

Values of Predictors for New Observations

New

Obs Weight

1 4000

Identifying Total Variation: What percentage of the total variation in highway fuel consumption can be explained by the linear correlation between weight and highway fuel consumption?

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