Regression analysis is a powerful statistical tool used to analyze and model the relationships between variables. It allows us to understand how changes in independent variables affect the value of a dependent variable. We will explore how to perform regression analysis in Microsoft Excel, specifically focusing on linear and multiple regression models.

## Accessing Regression Analysis in Microsoft Excel

Enable the Analysis ToolPak:

- Click on File in the Excel ribbon.
- Select Excel Options.
- Click on Add-Ins in the left sidebar.
- In the Manage box at the bottom, choose Excel Add-ins and click Go.

Once you’ve enabled the Analysis ToolPak, you will have access to a range of data analysis tools, including regression.

Data Analysis button will appear on Data ribbon. Under Data Analysis feature Regression function can be found.

## Regression Analysis in Excel

Prepare X & Y values in the following style.

Open Data Analysis and choose the Regression.

Fill the dialog box with ranges of your data:

- Input Y Range option: Select dependent variables,
- Input X Range option: Select independent variables,
- Output options specify how you would like the results to be displayed,
- Residuals contain options to draw the results as charts.

Following regression table will be created in new sheet as follows.

## Linear Regression in Excel

The linear regression function answers the question: “What value will a given phenomenon (dependent variable) take, depending on the value of another phenomenon (explanatory variable)?” Due to the term “linear”, a method which has a way to remove the explained phenomenon and the variable explanation is precisely linear.

To run the linear regression prepare your data.

Select the cells for y-values, then the ones for x-values. Check the labels.

Insert a scatter chart.

Right-click on the chart and choose Select Data.

Write the Series Name, choose the cells for X-values, and for Y-values.

Click Ok.

Right-click on any of the markers and select Add Trendline.

Check the Display Equation on Chart and the R-square value on chart.

You should have done a linear regression that looks like this:

## Multiple Regression in Excel

Multiple regression extends linear regression by considering the relationship between a dependent variable and multiple independent variables. Here’s how to perform multiple regression in Excel:

The first thing is having a data that could look something like this:

Choose the data you want to analyze on X values, and Y values. Select desired options, under the Residuals.

The multiple regression would look something like this:

Interpreting the Results

When interpreting the results of a regression analysis in Excel, consider the following:

### Regression Statistics

- Multiple R (Correlation Coefficient): A value higher than 0 indicates a positive relationship, with a higher number signifying a stronger relationship.
- R-squared (Coefficient of Determination): Indicates the proportion of values that fit the model, with higher values indicating a better fit.
- Adjusted R-squared: Particularly useful when you have multiple independent variables.
- Standard Error: A high standard error suggests less confidence in the analysis.
- Observations: The number of data points used in the analysis.

### ANOVA (Analysis of Variance)

- F-test and Significance F: These assess the statistical significance of the regression model.

### Residual Output

- Predicted Y: Values predicted by the model.
- Residuals: Measure how far actual data points deviate from predicted values.

To enhance the accuracy of your analysis, aim to minimize residual values.