# Multiple Linear Regression - Online Calculator

## Easily Analyze Data with Our Free Online Linear Regression Calculator

Our online calculator allows you to perform data analysis using simple linear regression, which involves only one independent variable, or multiple linear regression, which involves more than one independent variable. To use the calculator, you can either copy and paste your data from Excel or input it directly into the text fields, separating each variable with a comma, space, or line break.

Once you have entered your data, the calculator will provide you with a number of results, including various statistical measures such as the **R-squared** value and **F-statistic**. In addition, the calculator also includes multiple tests, such as the **Durbin-Watson**, **Jarque-Bera**, and **Breusch-Pagan** tests, to evaluate the assumptions of the model. These measures can help you evaluate the strength of the relationship between the variables and the reliability of the model.

In addition to these results, the calculator also generates scatter plots that show the predicted values of the dependent variable against the residuals, or the difference between the predicted values and the actual values. These plots can help you identify patterns and trends in the data, and can be useful for identifying potential outliers or errors in the data. Overall, our online calculator is a valuable tool for anyone interested in understanding and analyzing data using linear regression. And best of all, it's completely free to use! We hope you find it useful and encourage you to try it out for yourself.

For additional information on entering data, **see the documentation**

### Interpreting the Output of a Multiple Linear Regression Calculator

The results provided by the multiple linear regression calculator include a number of statistical measures that can help you understand and evaluate the model. Here is an explanation of each of the measures:

Dep. Variable: This refers to the dependent variable, or the variable that is being predicted by the model.**Method:** The method used to fit the model, in this case OLS (ordinary least squares).**R-squared:** This is a measure of how well the model fits the data. It ranges from 0 to 1, with a higher value indicating a better fit.**Adj. R-squared:** This is the adjusted R-squared, which takes into account the number of independent variables in the model. It is similar to R-squared, but may be more accurate when there are many independent variables.**F-statistic:** This is a measure of the overall significance of the model. A high F-statistic and a low probability value indicate that the model is a good fit for the data.**Log-Likelihood:** This is a measure of the overall fit of the model. A lower log-likelihood value indicates a better fit.**S:** This is the estimated error variance, or the average squared difference between the predicted values and the actual values. It is an estimate of the variance of the error term in the model. A lower value indicates a better fit.**AIC:** This is the Akaike Information Criterion, which is a measure of the goodness of fit of the model.**BIC:** This is the Bayesian Information Criterion, which is similar to the AIC but also takes into account the number of parameters in the model.**SSE:** This is the sum of squared errors, or the sum of the squared differences between the predicted values and the actual values. A lower SSE indicates a better fit.**SSR:** This is the sum of squared residuals, or the sum of the squared differences between the predicted values and the mean of the dependent variable.**SST:** This is the total sum of squares, or the sum of the squared differences between the actual values and the mean of the dependent variable.**N:** This is the number of observations in the data set.

Df Model: This is the degrees of freedom for the model, which is the number of independent variables.**Df Residuals:** This is the degrees of freedom for the residuals, which is the number of observations minus the number of independent variables.**coef:** This is the coefficient for each independent variable, which represents the estimated change in the dependent variable for each unit change in the independent variable.**std err:** This is the standard error of the coefficients, which represents the uncertainty in the estimates.**t:** This is the t-value for each coefficient, which represents the significance of the coefficient. A high t-value and a low p-value indicate that the coefficient is significant.**P>|t|:** This is the p-value for each coefficient in the model. The p-value represents the probability that the coefficient is not significant, or that the observed relationship between the dependent and independent variables could have occurred by chance. A low p-value (typically less than 0.05) indicates that the coefficient is significant and that the relationship between the variables is not likely to have occurred by chance.**Skew:** This is a measure of the symmetry of the data. A skew value of 0 indicates that the data is symmetrical, while a positive skew indicates that the data is skewed to the right and a negative skew indicates that the data is skewed to the left.**Kurtosis:** This is a measure of the peakedness of the data. A kurtosis value of 0 indicates that the data is normal, while a positive kurtosis indicates that the data is more peaked than normal and a negative kurtosis indicates that the data is less peaked than normal.**Durbin-Watson:** This is a test for autocorrelation, which is the presence of a correlation between the residuals of the model. A Durbin-Watson value between 0 and 2 indicates the presence of positive autocorrelation, while a value between 2 and 4 indicates the presence of negative autocorrelation.**Jarque-Bera:** This is a test for normality of the residuals. A low p-value indicates that the residuals are not normally distributed.**Breusch-Pagan:** This is a test for heteroscedasticity, which is the presence of unequal variance in the residuals. A low p-value indicates the presence of heteroscedasticity.

### Multiple Linear Regression Calculator FAQs

Here, you will find answers to some of the most common questions that users have about our calculator and linear regression in general. Whether you are a beginner or an experienced data analyst, we hope that this FAQ will provide you with the information you need to get the most out of our calculator. If you have a question that is not answered here, please feel free to contact us for further assistance.

Linear regression is a statistical method used to model the linear relationship between a dependent variable and one or more independent variables. It can be used to predict the value of the dependent variable based on the values of the independent variables.

The calculator uses a statistical method called ordinary least squares to fit a linear regression model to the data you provide. It then calculates various statistical measures and generates scatter plots to help you understand and analyze the data.

You can use any data that can be modeled using linear regression. This includes continuous and categorical data. You can either copy and paste your data from a spreadsheet (such as Excel) or enter it directly into the calculator using the text fields provided.

The R-squared value is a measure of how well the model fits the data. It ranges from 0 to 1, with a higher value indicating a better fit. A value of 0 means that the model does not explain any of the variance in the data, while a value of 1 means that the model explains all of the variance in the data.

To enhance your data analysis experience, the scatter plots show the predicted values of the dependent variable against the residuals, or the difference between the predicted values and the actual values. These plots can help you identify patterns and trends in the data, and can be useful for identifying potential outliers or errors in the data.

Linear regression assumes that the relationship between the dependent and independent variables is linear, that the errors are normally distributed and have constant variance, and that the errors are independent. It is important to check for the validity of these assumptions before interpreting the results of the model.

There are several statistical tests and plots that can be used to check the assumptions of linear regression. These include tests for normality of the residuals (such as the Jarque-Bera test), tests for autocorrelation (such as the Durbin-Watson test), and test for heteroscedasticity (such as the Breusch-Pagan test). The calculator provides some of these tests and plots to help you evaluate the assumptions of the model.

Yes, the calculator can be used for both simple linear regression (which involves only one independent variable) and multiple linear regression (which involves more than one independent variable). Simply enter the appropriate data.

Yes, the calculator is completely free to use! We hope that it is a valuable resource for anyone interested in understanding and analyzing data using linear regression.