# 12.3.5.1 - Example: Quiz and exam scores

12.3.5.1 - Example: Quiz and exam scoresData from a sample of 50 students were used to build a regression model using quiz averages to predict final exam scores. Construct a 95% confidence interval for the slope.

This example uses the Minitab file: Exam.mpx

We can use the coefficients table that we produced in the previous regression example using the exam data.

##### Coefficients

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

Constant | 12.1 | 11.9 | 1.01 | 0.315 | |

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

The general form of a confidence interval is sample statistic \(\pm\) multiplier(standard error).

We have the following:

- \(b_1\) (sample slope) is 0.751
- t multiplier for degrees of freedom of (50-2) = 48 is 2.01
- The standard error of the slope (\(SE_{b_1}\) is 0.141 from our table

The confidence interval is...

\begin{align} \text{sample statistic} &\pm \text{multiplier*standard error}\\ 0.751 &\pm 2.01 (0.141)\\ 0.751&\pm 0.283 \\ [0.468 &, 1.034] \end{align}

#### Interpret

I am 95% confident that the slope for this model is between 0.468 and 1.034 in the population.