Often you may execute **Multiple Regression Analysis **in Excel. But you may get troubled to understand the terms used in the regression analysis. In this article, Iâ€™ll discuss in detail how to interpret multiple regression results in Excel with a real-life example.

## 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

Letâ€™s say, you have the following dataset where Sales Report is given with **Unit Price**, **Promotion **(for advertisement), and **Sales**.

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

Whatever, to run the regression model, you need the **Data Analysis** command in Excel. If you donâ€™t have it in the ribbon by default, you may add it the following way.

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

- Next, check the
**Analysis ToolPak**and press**OK**.

Now, youâ€™re ready to run the regression model for the above dataset in Excel.

- Initially, select the
**Data Analysis**command from the**Data**tab.

- And, pick the
**Regression**tool.

- Later, specify the
**Input Y Range**as**$E$4:$E$15**and**Input X Range**as**$C$4:$D$15**. Also, check the box before**Labels**and press**OK**.

Eventually, youâ€™ll get the following output.

## 1. Interpreting Results of Multiple Regression Statistics Table in Excel

If you closely look at the upper portion of the regression output, you’ll get a table titled **Regression StatisticsÂ **as shown in the below screenshot.

Now, let’s try 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 understand the term better.

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 youâ€™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:**Simply, the Standard error tells about the precision of your multiple regression analysis.**Observations:**It shows the number of products which is 11.

## 2. Interpreting Regression Results of ANOVA Table in Excel

Moreover, 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, youâ€™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 there is a significant relationship between the*Unit Price*and*Promotion*(x values) and*Sales*(y values).

## 3. Interpreting Results of Multiple Regression Coefficients Table in Excel

Let’s have a look at the last portion where you have to know the following terms.

**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:**Simply 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**

## Conclusion

Thatâ€™s the end of todayâ€™s session. I firmly believe this article will be highly beneficial for you to interpret the multiple regression results found in Excel. Anyway, donâ€™t forget to share your thoughts.

## 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 ExcelÂ
- How to Interpret Regression Results in Excel

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