While working with** Microsoft Excel,** sometimes you may need to create a new data point from the given range of known data points. In such a situation, you might accomplish **linear regression in Excel.** You also can **interpret the linear regression result**. This is an easy time-saving task also. Today, in this article, weâ€™ll learn **two **quick and suitable steps to interpret the linear regression results in **Excel **from the web effectively with appropriate illustrations.

**Table of Contents**hide

## Download Practice Workbook

Download this practice workbook to exercise while you are reading this article.

## Introduction to Linear Regression in Excel

**Linear regression** is a method of modeling the connection between a scalar answer and one or more explanatory variables in statistics (also known as dependent and independent variables). Simple linear regression is used when there is only one explanatory variable; **multiple linear regression** is used when there is more than one.

The mathematical expression of Linear Regression is:

**y = mx + c + b**

Where

**x** is an independent variable.

**y** is a dependent variable.

When all **x** variables are equal to** 0, c** is the** Y**-intercept, which is the expected mean value of **y**. Itâ€™s the point on a regression graph where the line crosses the **Y** axis.

**m** is the slope of a regression line.

**b **is the random error term.

Because predictors are never fully precise in real life, the linear regression equation always has an error term. However, certain systems, such as **Excel**, calculate the error term behind the scenes. So, in **Excel**, you use the least squares approach to perform linear regression and look for coefficients **m** and **c** such that:

**y = mx + c**

**y = slope*x + Intercept**

## 2 Easy Steps to Interpret Linear Regression Results in Excel

Letâ€™s assume we have an **Excel **large worksheet that contains the information about the COVID test result. From our dataset, we will interpret the **Linear Regression** results in** Excel **by using the **Data Analysis** command. Hereâ€™s an overview of the dataset for todayâ€™s task.

### Step 1: Using Data Analysis Command to Interpret Linear Regression Results in Excel

We will use the **Data Analysis** command to interpret the **Linear Regression** result in excel. This is an easy task and time-saving also. Letâ€™s follow the instructions below to interpret the Linear Regression!

- First of all, create an
**Excel**After that, from your**Data**tab, go to,

**Data â†’ Analysis â†’ Data Analysis **

- After pressing on the
**Data Analysis**option, a**Data Analysis**dialog box will appear in front of you. From that dialog box, firstly, select**Regression**under the drop-down list named**Analysis Tools.**At last, press the**OK**option.

- As a result, a
**Regression**dialog box will appear in front of you. From the**Regression**dialog box, firstly, type**$C$5:$C$15**in the**Input Y Range**and type**$D$5:$D$15**in the**Input X Range**under the Input menu. Secondly, type**$F$4**in the**Output Range**drop-up box under the**Output options**Thirdly check the**Residuals**option from the**Residuals**menu**.**At last, press the**OK**option.

- After pressing the
**OK**option, you will be able to analyze the Linear Regression results.

### Step 2: Interpret the Linear Regression Results in Excel

In this step, we will analyze the Linear Regression result. The summary of the** Linear Regression** is given in the below screenshot:

Now, we will describe the meanings of the information.

**Multiple R:**

**Multiple R** is the **Correlation Coefficient**. It calculates the strength of a linear relationship between two variables. The correlation coefficient can have any value between -1 and 1, with the absolute value indicating the strength of the association.

- 1 uses for the strong positive relationship.
- -1 uses for the strong negative relationship.
- 0 uses for the no relationship

**R Square:**

**R Square** is the **Coefficient of Determination**. It is used to calculate the goodness of fit. It displays the number of points that fall on the regression line. The value of **R ^{2}** is calculated using the total sum of squares, or more accurately, the sum of the original dataâ€™s squared deviations from the mean.

**Adjusted R Square:**

Itâ€™s the **R square** multiplied by the number of **independent variables** in the model. For **multiple regression analysis**, this number applies in lieu of **R square**.

**Standard Error:**

Another goodness-of-fit metric that indicates the precision of your regression analysis; the lower the value, the more confident you can be in your regression equation. **Standard Error** is an absolute metric that reflects the average distance that the data points fall from the regression line, whereas **R ^{2}** represents the proportion of the variation of the dependent variable that is explained by the model.

**Observations:**

The total number of observations of your model data.

**Analysis of Variance (ANOVA)**

The second table data is the **Analysis of Variance (ANOVA)**. The **ANOVA **table is:

Undoubtedly, it divides the sum of squares into discrete components that reveal the levels of variability in your regression model:

**df** means the number of degrees of freedom.

**SS** means the sum of squares.

**MS** stands for mean square.

The **F** statistic, often known as the F-test, is used to test the null hypothesis. It determines the modelâ€™s overall significance.

For a simple **linear regression** study in **Excel**, the **ANOVA **section is rarely used, but the last component should be carefully examined. The **Significance F** value indicates how trustworthy your results are. Your model is acceptable if **Significance F** is less than **0.05** (5 percent). You should probably choose another independent variable if it is bigger than **0.05**.

Coefficients are the most useful component in this section. In Excel, it allows you to create a linear regression equation:

**y = mx + c**

**Read More:** **How to Interpret Multiple Regression Results in Excel**

## Things to Remember

âžœ While a value can not found in the referenced cell, the **#N/A** error happens in **Excel**.

## Conclusion

I hope all of the suitable methods mentioned above to **interpret linear regression results **will now provoke you to apply them in your **Excel **spreadsheets with more productivity. You are most welcome to feel free to comment if you have any questions or queries.