## What Is Multiple Regression?

When the number of independent variables is two or more while doing** linear regression**, it is called** multiple linear regression analysis****.** The equation for calculating **multiple regression analysis** is as follows.

`y=b+b`

_{1}`X`

_{1}`+b`

_{2}`X`

_{2}`+....b`

_{n}`X`

_{n}

Where

**Y** is the dependent variable

**b** is the intercept

**X _{1}** and

**X**are the independent variables

_{2}**b _{1}** and

**b**are coefficients of the corresponding independent variables.

_{2}## How Can You Do Multiple Regressions in Excel

We have the following sample dataset where Sales Report is given with **Unit Price**, **Promotion **(for advertisement) and **Sales**.

We need to run the multiple regression model to find the relationship between the dependent variable (*Sales*) and the independent variables (*Unit Price* and *Promotion*).

To run the regression model, you need the **Data Analysis** command. If you don’t have it in the ribbon by default, you may add it the following way.

- Go to
**File**>**Options**. - In the
**Excel Options**, navigate to the**Add-ins**and press the**Go**button.

- Check the
**Analysis ToolPak**and press**OK**.

You’re ready to run the regression model for the above dataset.

- Select the
**Data Analysis**command from the**Data**tab.

- Pick the
**Regression**tool.

- Specify the
**Input Y Range**as**$E$4:$E$15**and**Input X Range**as**$C$4:$D$15**. Check the box**Labels**and press**OK**.

You’ll get the following output.

**Example 1 – **Interpreting Results of Multiple Regression Statistics Table in Excel

If you look at the upper portion of the regression output, you’ll see a table titled **Regression Statistics** as shown in the following image.

Here’s how to understand the terms.

**Multiple R (Correlation Coefficient): Multiple R**refers to the degree of linear relationship among the variables. The following table may help you to better understand the term.

Value of Multiple R | Refers to |
---|---|

1 | Strong positive relationship |

0 | No relationship |

-1 | Strong negative relationship |

**R Square (Coefficient of Determination):****R Square**reveals the goodness of fit. That means how many points fit with the regression line. The higher the value of R Square, the better-fitted the regression line you’ll get. Here, the value of R Square represents an excellent fit as it is 0.94. It means that 94% variation in the dependent variable can be explained by the independent variable. In the case of multiple regression relationships, you have to keep attention to the Adjusted R square.**Adjusted R Square: Adjusted R Square**is fruitful when you have two or more independent variables. As it provides the comparison among the variables which one is more important than the other. The value will be higher than the R Square if a new independent variable improves the model or vice versa. In this dataset, the value of the*Adjusted R Square*is 0.92. That means 92% of the points fit the regression line.**Standard Error:**The Standard error tells us about the precision of our multiple regression analysis.**Observations:**It shows the number of products which is 11.

**Example 2 – **Interpreting Regression Results of ANOVA Table in Excel

In the middle of the output, you’ll see the **ANOVA (Analysis of Variance) Table**.

The terms used in the table are as follows.

**df (degrees of freedom): df**refers to degrees of freedom. It can be calculated using the**df=N-k-1**formula where**N**is the sample size and**k**is the number of regression coefficients.**SS (Sum of Squares):**The*Sum of Squares*is the square of the difference between a value and the mean value. The higher the value of the**Sum of Squares**refers to higher variation in the values or vice-versa.**MS (Mean Squares): Mean Squares**is mainly the mean of the square of the variation of an individual value and the mean value of the set of observations.**F (F-test): F**or**F statistic**provides the overall importance of the regression model for the null hypothesis. If you divide the**MS**of regression by the**MS**of Residual, you’ll get the**F-test**.**Significance F: Significance F**is a crucial term to find the output of your model whether it is statistically significant or not. When the value of the**Significance F**is not greater than 0.05, the independent variables have a statistically significant relationship with the dependent variable. Here, it is 0.00001 which represents that there is a significant relationship between the*Unit Price*and*Promotion*(x values) and*Sales*(y values).

**Example 3 – **Interpreting Results of Multiple Regression Coefficients Table in Excel

**Coefficients:**Coefficients are calculated using the least square method. In this example, the regression equation will be-

`y(Sales)=-1642.04 + 9.91*Unit Price + 8.13*Promotion`

**Standard Error:**It is the standard deviation of least square estimates.**t Stat: t Stat:**refers to the coefficient being equal to zero in the case of the null hypothesis.**P-value: The P-value**shows the statistically significant relationship between the independent and dependent variables. Here,**P-value**for*Unit Price*is 0.000003 which is below 0.05. So,*Unit Price*is statistically significant with the*Sales*.**Lower 95%:**It means the lower limit when the confidence interval is 95%.**Upper 95%:**It is the upper limit of the confidence interval.

**Read More:** How to Calculate P Value in Linear Regression in Excel

**Download Practice Workbook**

## Related Articles

- How to Do Simple Linear Regression in Excel
- How to Do Logistic Regression in Excel
- How to Plot Least Squares Regression Line in Excel
- How to Interpret Linear Regression Results in Excel
- How to Interpret Regression Results in Excel

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