Regression Analysis

Jay Arthur
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When to use regression analysis

The purpose of regression analysis is to evaluate the effects of one or more independent variables on a single dependent variable.

Regression arrives at an equation to predict performance based on each of the inputs.

To run Regression Analysis using the QI Macros

1. Select the labels and data.
2. Select Anova and Analysis Tools then Regression Analysis.
3. Input the confidence level (e.g., 0.95).
4. Evaluate the Rsquared (>0.80 is a good fit).
5. Evaluate the F and p values
6. Get the equation for the fitted data.
7. Use the equation to predict other values.

Here is an example of the results of running regression analysis in Excel using the QI Macros.

1. Select the data

2. Click on the QI Macros menu and
choose Anova then Regression Analysis:

3. Enter the confidence level (e.g., 0.95) and the QI Macros with Excel will generate the results.

4. Evaluate the R Square value (0.951).

Analysis: If R Square is greater than 0.80, as it is in this case, there is a good fit to the data. Some statistics references recommend using the Adjust R Square value.

Interpretation: R Square of .951 means that 95.1% of the variation in salt concentration can be explained by roadway area. The adjusted R Square of .949 means 94.9%.

5. Evaluate the F and p Values

In this case, the Signficance F < 0.05, so reject the null hypothesis that the variation of these two data sets are unrelated. The p value for % Paved Roadway, 3E-13 < 0.05, rejects the null hypothesis that they are unrelated.

6. Get the equation for the data.

Click on the line fit plot (below) and right click on one of the %paved roadway points.
Select Add Trendline:

Then choose linear trendline and click on Options to show the equation:

Excel will display the fitted equation onto the chart (Salt concentration = 17.547*(%roadway area)+2.6765).

7. Use the equation for prediction and estimation.

Using the equation, Salt concentration = 17.547*(%roadway area)+2.6765, you could predict the salt concentration if the percent of roadway was 1% as Salt concentration = 17.547 (1) +2.6765 = 20.2235 mg/l.

The QI Macros Statistical Process Control software takes two or more rows/columns of data and formats them in the ideal way for Excel to process them which saves you from having to figure out how to use Excel's Data Analysis Toolpak. Here are some of the statistical analyses you can run.

• Single Regression Example
• Multiple Regression Example
• Correlation Example
• Covariance Example
• Other forms of hypothesis testing in Excel

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