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, we’ll learn two quick and suitable steps to interpret the linear regression results in Excel from the web effectively with appropriate illustrations.
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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
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. It’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
Let’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. Here’s an overview of the dataset for today’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. Let’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 → Analysis → 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 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 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 R2 is calculated using the total sum of squares, or more accurately, the sum of the original data’s squared deviations from the mean.
Adjusted R Square:
It’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.
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 R2 represents the proportion of the variation of the dependent variable that is explained by the model.
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 model’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
➜ While a value can not found in the referenced cell, the #N/A error happens in Excel.
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.