# Linear Regression

Contents Model the linear relationship between numeric response and one or more explanatory variables by fitting a linear regression model.

## Details

This module will create a linear model, modelling one dependent variable as a linear combination of one or more independent variables. It is important to note that linear regression assumes independence, linearity, normality and homoscedasticity of data. If these assumptions are violated, then the regression might be biased, thus it is important to test these assumptions before performing linear regression.

Linear regression is often fitted to the data in order to obtain a predictive model, which then can be used to estimate the value of response variable Y when only predictor (X) is known. Linear regression can also be used to assess the relationship between different variables in a dataset and analyse whether the variance in some variables can be explained or modelled by linear combinations of other variables.

## Output

The example below shows how to use the Linear Regression module to create a simple regression model of petal length (dependent/response variable) and petal width (predictor/independent variable).

The output below shows the linear regression results. It also includes a graph of residuals plotted against the fitted values. The module output is the summary of the linear model results. The summary function provides us with a wealth of information related to the linear model, including t-test, F-test, R-squared, residual, and significance values. More details on this can be found in the R documentation for `lm`.

From the example output, we see that the linear model intercept is equal to 1.09, and the petal width coefficient is equal to 2.23, thus we can write our linear equation as follows:

``````petal_length = 1.09 + 2.23 * petal_width
`````` ## Parameters

Variable name Required Constraints Description
outcome_var Yes Column with data type one of: Decimal, Integer The dependent variable to be modeled by the selections in `model_var1`, `model_var2`, `...`
model_var1 Yes Any column other than the column chosen for outcome_var. The first independent variable or predictor variable to include in the linear model.
model_var2 No Any column other than the column chosen for outcome_var. An optional second predictor variable.
model_var3 No Any column other than the column chosen for outcome_var. An optional third predictor variable.
model_var4 No Any column other than the column chosen for outcome_var. An optional fourth predictor variable.
model_var5 No Any column other than the column chosen for outcome_var. An optional fifth predictor variable.
include_intercept Yes Boolean Whether to include an intercept term in the model