Exercise 12.7.1 Simple Regression

Data has been collected on a process where a single predictor affects a continuous Response variable. The data has not been collected in time order. Conduct the appropriate Regression analysis and answer the questions below.

The data in File 12 Regression.xlsx worksheet Exercise1.

- What order of equation best fits the data and is significant?
- How much of the variation in the Response can be explained by changes in the Predictor?
- Are there any unusual data points in the study and are they an issue?
- Using this process could we reasonably expect a data point to appear at 60 for the predictor and 200 for the response?

- Click Stat<<Regression<<Fitted Line Plot
- Enter the column headings as shown.
- Click on the radio button to use the Cubic model.
- Click OK to execute the procedure.

If you go to the Session Window you will see that the Cubic term is not significant and that a quadratic model should be fitted. We can do this using the Assistant.

The Model Selection Report shows that one data point had a large residual.

- Click Assistant<<Regression.
- Click on the Simple Regression box.
- Enter the column headings as shown.
- Leave ‘Choose for me’ as the selected choice.
- Click OK to produce the five page report.

The Diagnostic Report again shows the unusual data point. It can be seen it is not two far away from the rest of the data.

Reference lines have been added to the Prediction Plot on the Prediction Report. We can reasonably expect a data point to appear at 60 for the predictor and 200 for the response and this point lies within the prediction interval

On the top left of the Summary Report we are told that the quadratic model is significant and that 95.81% of the changes in the response can be explained by changes in the predictor.