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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 ...

$2.19