# Multiple Regression Analysis

## When to Use Multiple Regression Analysis

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

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

### Multiple Regression Analysis Example

Let's say we want to know if customer perception of shampoo quality (dependent variable) varies with various aspects of geography and shampoo characteristics: Foam, Scent, Color or Residue (independent variables).

#### To Conduct Multiple Regression Analysis Using QI Macros for Excel

- Select two to sixteen columns of data with the dependent variable in the first (or last) column:
- QI Macros will ask you which column the dependent variable (Y Value) is in. In this example, its in the first column:
- QI Macros will perform the calculations and display the results for you:

*This sample data is found in QI Macros Test Data > Matrix Plot.xlsx > Shampoo Data*

### Evaluate the R Square value (0.800)

**Analysis:** If R Square is greater than or equal to 0.80, as it is in this case, there is a good fit to the data.

### Evaluate the p value

The null hypothesis is that there is no correlation. (H0 = no correlation.) Looking at the p values for each independent variable, Region, Foam and Residue are less than alpha (0.05), so we reject the null hypothesis and can say that these variables impact quality. Scent and color p values are greater than 0.05, so we cannot reject the null hypothesis (accept the null hypothesis) that there is no correlation and we can't say they directly impact quality.

### Use the Equation for Prediction and Estimation

Using the equation below, you could predict the perception of shampoo quality based on the independent variables. Again, Region, Foam and Residue seem to have the greatest impact on the perception of quality.

y = 90.192 -3.859*Region +1.817*Foam +1.035*Scent +0.233*Color -4.001*Residue

### Residuals Output, Probability Output and Charts

In addition to the Summary Output above, QI Macros also calculates residuals and probability data and draws several charts for you.

Please note that the straight lines on your first chart (Region) represent the Upper and Lower Prediction Intervals, while the more curved lines are the Upper and Lower Confidence Intervals

Confidence Intervals provide a view into the uncertainty when estimating the *mean*, while Prediction Intervals account for variation in the Y values *around the mean*.

The 95% and 99% Confidence Levels reference when your alpha value is set at .05 (95%) or .01 (99%). This provides you with information on how the confidence level can impact your results, depending on where alpha is set.

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