Multiple Regression & Stepwise Selection of Predictor ...



Multiple Regression & Stepwise Selection of Predictor Variables

This handout continues to use the car dataset to discuss several additional aspects of multiple regression. The process of choosing a multiple regression model can be broken into several steps, and these are briefly discussed below. In addition this handout describes the mathematical definition and interpretation of several of the quantities in the JMP output.

We produce a slightly different analysis than that in the previous handout with this data.

Step 1: Perform exploratory analyses. Here’s one example

GP1000M City By Horsepower

[pic]

Both the best linear fit and a smooth curve (“spline”) through the data are shown.

Summary of Fit (for the linear fit)

RSquare 0.690

Residual Plot:

[pic]

The scatterplot, as well as the residual plot, suggest trying to transform to Log(Horsepower).

GP1000M City By Log(horsepr.)

[pic]

Both the best linear fit and a smooth curve through the data are shown.

They nearly agree; visually showing the line is a good fit.

Linear Fit: GP1000M City = -65.52 + 54.792 Log (HP)

Summary of Fit

|RSquare |0.7697 |

|Root Mean Square Error |4.1941 |

|Observations |107 |

Analysis of Variance

|Source |DF |Sum of Squares |Mean Square |F Ratio |

|Model |1 |6172.5 |6172.5 |350.91 |

|Error |105 |1847 |17.59 |Prob > F |

|C. Total |106 |8019.5 | ||t| |

|Intercept | |-65.52 |6.0653 |-10.80 | ................
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