# Solve: Linear Regression Modelling

Scenario: A sample of twenty automobiles was taken, and the miles per gallon (MPG), horsepower and total weight were recorded. Develop a linear regression model to predict MPG using horsepower as the only independent variable. Develop another model with weight as the independent variable. Which of these two models is better? Explain.

MPG Horsepower Weight

44 67 1844

44 50 1998

40 62 1752

37 66 1797

34 63 2199

35 90 2404

32 99 2611

30 63 3236

28 91 2606

26 94 2580

26 88 2507

25 124 2922

22 97 2434

20 114 3248

21 102 2812

18 114 3382

18 142 3197

16 153 4380

16 139 4036

The estimated regression model is

MPG = _____ *Horse Power

For a unit increase in horse power , the MPG, decrease by _____ units .

The model adequacy measure R^2 = _____. Thus ___ % variability in MPG can be explained by the regression model.

The estimated regression model is

MPG = _____ - _____ *Weight

For a unit increase in Weight , the MPG, decrease by _____ units .

The model adequacy measure R^2 = _____ . Thus ___ % variability in MPG can be explained by the regression model with weight as the independent variable.

#### Solution Preview

Please see the attached file for proper formatting.

(Note: The data provided contains 19 values only)

First , we develop a linear regression model to predict MPG using horsepower as the only independent variable.

We develop a regression equation of the form Y = a + bX

- where Y = MPG, X= horsepower

- a and b are constants which are calculated using the following equations

We also calculate the value of R^2 by first calculating the value of r and then squaring it.

Horsepower MPG

(X) (Y) XY X2 Y2

67 ...