Multiple regression equation with 3 variables calculator

Q: How do you write a multi regression equation example?

Let us consider just the case of X with X2. With these variables, the usual multiple regression equation, Y = a + b1X1 + b2X2, becomes the quadratic polynomial Y = a + b1X + b2X2. This is still considered a linear relationship because the individual terms are added together.

Interpreting results

Using the formula Y = mX + b:

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Interpreting results
Graphing linear regression
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Want to see what regression analysis looks like from start to finish?
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Multiple Linear Regression (MLR) Calculation
Related Calculators:
How do you write a regression equation with multiple variables?
Can linear regression have 3 variables?
What is the formula for multiple regression?
How do you write a multi regression equation example?

The linear regression interpretation of the slope coefficient, m, is, "The estimated change in Y for a 1-unit increase of X."
The interpretation of the intercept parameter, b, is, "The estimated value of Y when X equals 0."

The first portion of results contains the best fit values of the slope and Y-intercept terms. These parameter estimates build the regression line of best fit. You can see how they fit into the equation at the bottom of the results section. Our guide can help you learn more about interpreting regression slopes, intercepts, and confidence intervals.

Use the goodness of fit section to learn how close the relationship is. R-square quantifies the percentage of variation in Y that can be explained by its value of X.

The next question may seem odd at first glance: Is the slope significantly non-zero? This goes back to the slope parameter specifically. If it is significantly different from zero, then there is reason to believe that X can be used to predict Y. If not, the model's line is not any better than no line at all, so the model is not particularly useful!

P-values help with interpretation here: If it is smaller than some threshold (often .05) we have evidence to suggest a statistically significant relationship.

Finally the equation is given at the end of the results section. Plug in any value of X (within the range of the dataset anyway) to calculate the corresponding prediction for its Y value.

Graphing linear regression

The Linear Regression calculator provides a generic graph of your data and the regression line.

While the graph on this page is not customizable, Prism is a fully-featured research tool used for publication-quality data visualizations. See it in action in our How To Create and Customize High Quality Graphs video!

Graphing is important not just for visualization reasons, but also to check for outliers in your data. If there are a couple points far away from all others, there are a few possible meanings: They could be unduly influencing your regression equation or the outliers could be a very important finding in themselves. Use this outlier checklist to help figure out which is more likely in your case.

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Liked using this calculator? For additional features like advanced analysis and customizable graphics, we offer a free 30-day trial of Prism

Some additional highlights of Prism include the ability to:

Use the line-of-best-fit equation for prediction directly within the software
Graph confidence intervals and use advanced prediction intervals
Compare regression curves for different datasets
Build multiple regression models (use more than one predictor variable)

Looking to learn more about linear regression analysis? Our ultimate guide to linear regression includes examples, links, and intuitive explanations on the subject.

Prism's curve fitting guide also includes thorough linear regression resources in a helpful FAQ format.

Both of these resources also go over multiple linear regression analysis, a similar method used for more variables. If more than one predictor is involved in estimating a response, you should try multiple linear analysis in Prism (not the calculator on this page!).

Want to see what regression analysis looks like from start to finish?

Check out our video below on How to Perform Linear Regression in Prism.

Examine the relationship between one dependent variable Y and one or more independent variables Xi using this multiple linear regression (mlr) calculator.

Multiple Linear Regression (MLR) Calculation

Examine the relationship between one dependent variable Y and one or more independent variables Xi using this multiple linear regression (mlr) calculator.

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Formula Used: Y = a + b1X1 + b2X2 + ... + bnXn Where, a - Y intercept point b1, b2, ... , bn - Slope of X1, X2, ... , Xn respectively

The calculation of multiple linear regression (mlr) equation is made easier here.

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Gaussian Error Function (erf)

Instructions: You can use this Multiple Linear Regression Calculator to estimate a linear model by providing the sample values for several predictors \((X_i)\) and one dependent variable \((Y)\), by using the form below:

Multiple Linear Regression Calculator

More about this Multiple Linear Regression Calculator so you can have a deeper perspective of the results that will be provided by this calculator. Multiple Linear Regression is very similar to Simple Linear Regression, only that two or more predictors \(X_1\), \(X_2\), ..., \(X_n\) are used to predict a dependent variable \(Y\). The multiple linear regression model is

\[ Y = \displaystyle \beta_0 + \beta_1 X_1 + \beta_2 X_2 + ... + \beta_n X_n + \epsilon\]

where \(\epsilon\) is the error term that has the property of being normally distributed with mean 0 and constant variance \(\epsilon ~ N(0, \sigma^2)\). After providing sample values for the predictors \(X_1\), \(X_2\), ..., \(X_n\) and the response variable \(Y\), estimates of the population slope coefficients are obtained by minimizing the total sum of squared errors . The estimated model is expressed as:

The expression that is used to compute the odds for the occurrence of an event, \(p\), given its probability is shown below:

\[ \hat Y = \displaystyle \hat\beta_0 + \hat\beta_1 X_1 + \hat\beta_2 X_2 + ... + \hat\beta_n X_n\]

If, on the other hand, you want to use only one predictors, you can use this simple linear regression calculator instead.

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How do you write a regression equation with multiple variables?

y = mx1 + mx2+ mx3+ b M= slope of the regression. X1=first independent variable of the regression. The x2=second independent variable of the regression. The x3=third independent variable of the regression.

Can linear regression have 3 variables?

Linear regression can only be used when one has two continuous variables—an independent variable and a dependent variable.

What is the formula for multiple regression?

The multiple regression equation explained above takes the following form: y = b₁x₁ + b₂x₂ + … + b_nx_n + c. Here, b_i's (i=1,2…n) are the regression coefficients, which represent the value at which the criterion variable changes when the predictor variable changes.

How do you write a multi regression equation example?

Let us consider just the case of X with X². With these variables, the usual multiple regression equation, Y = a + b₁X₁ + b₂X₂, becomes the quadratic polynomial Y = a + b₁X + b₂X². This is still considered a linear relationship because the individual terms are added together.