# Linear Regression

## Introduction

Linear regression model is a statistical model with an assumption that linear relationships are there between explanatory variable and a response variable.

## How to Access?

There are two ways to access. One is to access from 'Add' (Plus) button.

![](https://2850417076-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M4HLCK3olgduYoe3RVS%2F-M4oMvCUDQwHTJ0eWi_f%2F-M4oNHX1109aRthYeMfG%2Flm_add.png?generation=1586795491316344\&alt=media)

Another way is to access from a column header menu from a numeric column.

![](https://2850417076-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M4HLCK3olgduYoe3RVS%2F-M4oMvCUDQwHTJ0eWi_f%2F-M4oNHX6vTOEn9oYqMuK%2Flm_cols.png?generation=1586795491485179\&alt=media)

## How to Use?

### Column Selection

There are two ways to set what you want to predict by what variables.

![](https://2850417076-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M4HLCK3olgduYoe3RVS%2F-M4oMvCUDQwHTJ0eWi_f%2F-M4oNHX8hU2ZcltwKcYd%2Flm_col_select.png?generation=1586795491061123\&alt=media)

If you are on "Select Columns" tab, you can set them by column selector.

![](https://2850417076-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M4HLCK3olgduYoe3RVS%2F-M4oMvCUDQwHTJ0eWi_f%2F-M4oNHXAKxLH5C84J2CV%2Flm_custom.png?generation=1586795491125683\&alt=media)

If you are on "Custom" tab, you can type a formula directly.

### Train Test Split

![](https://2850417076-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M4HLCK3olgduYoe3RVS%2F-M4oMvCUDQwHTJ0eWi_f%2F-M4oNDzLGK7ZU1RCNZk_%2Ftrain_test_split.png?generation=1586795485645143\&alt=media)

You can split the data into training and test to evaluate the performance of the model. You can set

* Test Data Set Ratio - Ratio of test data in the whole data.
* Random Seed to Split Training/Test - You can change random seed to try other training and test data combination.

### Parameters

* A Vector to Subset Data (Optional) - "subset" parameter of lm function.
* Weight Vector (Optional) - "weights" parameter of lm function.
* How to treat NA? (Optional) - "na.action" parameter of lm. function. The default is "na.fail". This changes the behaviour of NA data. Can be one of the following.
  * "na.omit"
  * "na.fail"
  * "na.exclude"
  * "na.pass"
  * NULL
* Which method to apply? (Optional) - "method" parameter of lm function. The default is "qr". The method to be used in fitting the model. This can be
  * "qr"
  * "model.frame"
* Return Model Ojbect (Optional) - "model" parameter of lm function.
* Return Model Matrix X (Optional) - "x" parameter of lm function.
* Return Model Matrix Y (Optional) - "y" parameter of lm function.
* Return QR Decomposition (Optional) - "qr" parameter of lm function. The default is TRUE. If qr should be returned.
* Allow Singular Fit - "singular.ok" of lm parameter of lm function. The default is TRUE. Whether only one observation fitting should be accepted.
* Offset (Optional) - "offset" of lm parameter of lm function. Already known components for linear predictors during fitting.

Take a look at the [reference document](https://stat.ethz.ch/R-manual/R-devel/library/stats/html/lm.html) for the 'lm' function from base R for more details on the parameters.

## How to Read Summary

![](https://2850417076-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M4HLCK3olgduYoe3RVS%2F-M4oMvCUDQwHTJ0eWi_f%2F-M4oNHXIPwTIabqGwg63%2Flm_summary.png?generation=1586795491386953\&alt=media)

Once you run it, you will see summary info like this.

### Summary of Fit

* R Square - The percent of variance explained by the model.
* R Square Adj - R Square adjusted based on the degrees of freedom.
* Root Mean Square Error - The square root of the estimated residual variance.
* F Ratio - F-statistic.
* P Value - p-value from the F test, describing whether the full regression is significant.
* DF - Degrees of freedom used by the coefficients.
* Log Likelihood - The data's log-likelihood under the model.
* AIC - The Akaike Information Criterion.
* BIC - The Bayesian Information Criterion.
* Deviance - Deviance.
* Residual DF - Residual degrees of freedom.

### Parameter Estimates

* Term - The term in the linear model being estimated and tested.
* Estimate - The estimated coefficient.
* Std Error - The standard error from the linear model.
* t Ratio - t-statistic.
* P Value - Two sided p-value.
* Conf Low - Lower bound of 95% confidence interval.
* Conf High - Upper bound of confidence interval.

## Step-by-step

Here's a step-by-step tutorial guide on how you can build, predict and evaluate linear regression model.

* [Introduction to Linear Regression Model in Exploratory](https://blog.exploratory.io/introduction-to-linear-regression-model-in-exploratory-a46e90d62f7d)