# 3.4.3.1 - Minitab: SLR

3.4.3.1 - Minitab: SLR##
Minitab^{®}
– Simple Linear Regression

We previously created a scatterplot of quiz averages and final exam scores and observed a linear relationship. Here, we will use quiz scores to predict final exam scores.

- Open the Minitab file: Exam.mwx (or Exam.csv)
- Select
*Stat > Regression > Regression > Fit Regression Model...* - Double click
*Final*in the box on the left to insert it into the*Responses (Y)*box on the right - Double click
*Quiz_Average*in the box on the left to insert it into the*Continuous Predictors (X)*box on the right - Click
*OK*

This should result in the following output:

#### Regression Equation

Final = 12.1 + 0.751 Quiz_Average

#### Coefficients

Term | Coef | SE Coef | T-Value | P-Value | VIF |
---|---|---|---|---|---|

Constant | 12.1 | 11.9 | 1.01 | 0.3153 | |

Quiz_Average | 0.751 | 0.141 | 5.31 | 0.000 | 1.00 |

#### Model Summary

S | R-sq | R-sq(adj) | R-sq(pred) |
---|---|---|---|

9.71152 | 37.04% | 35.73% | 29.82% |

#### Analysis of Variance

Source | DF | Adj SS | Adj MS | F-Value | P-Value |
---|---|---|---|---|---|

Regression | 1 | 2664 | 2663.66 | 28.24 | 0.000 |

Quiz_Average | 1 | 2664 | 2663.66 | 28.24 | 0.000 |

Error | 48 | 4527 | 94.31 | ||

Total | 49 | 7191 |

#### Fits and Diagnostics for Unusual Observations

Obs | Final | Fit | Resid | Std Resid | |
---|---|---|---|---|---|

11 | 49.00 | 70.50 | -21.50 | -2.25 | R |

40 | 80.00 | 61.22 | 18.78 | 2.03 | R |

47 | 37.00 | 59.51 | -22.51 | -2.46 | R |

*R Large residual*

#### Interpretation

In the output in the above example we are given a simple linear regression model of Final = 12.1 + 0.751 Quiz_Average

This means that the y-intercept is 12.1 and the slope is 0.751.