### R Tutorial 15.0

In the previous blog, we learned making a linear regression model. The only thing we left was necessary testing of certain assumption. Testing these assumptions is equivalent to health check-up of the model ; a healthy model is supposed to be a robust model.

Let's play doctor-doctor!

The artcile has been written in continuation of our previous article :

**Linear Regression with R**

There are 4 (few statisticians consider 5) important assumptions for Linear Regression :

###

### 1. Assumption of Linearity :

The assumption of linearity is checked during the course of modeling it self, by plotting x-y scatter plot of dependent and one of the independent variables at a time. We check for a linear pattern and if necessary, we do the transformations (e.g. log, square, roots etc.)### 2. No Multicollinearity:

This is also considered as assumption for a linear regression model, I consider it to be important, but not part of 4 main assumptions. Anyways, in order to satisfy it, we check the VIF and drop the variables during the course of modeling itself.

**Related post ::**

**How multicollinearity can be hazardous to your model ?**

**Above two assumptions have been checked in the previous article itself :**

### Linear Regression with R

### 3. Normality of residual term :

It is time to do a post-model assumption check. There are two ways to check the normality or residual term :

**Method 1 :**

layout(matrix(c(1), 1, 1))

qqplot(model_2, main = "QQ Plot")

All the residuals should lie on the straight red line (as much as possible) and within the dotted red lines zone to ensure the normality or error.

**Method 2 :**

residuals = residuals(model_2)

shapiro.test(residuals)

The null hypothesis of the Shapiro-Wilk test in normality, and hence in order to not being able to reject the null hypothesis ( simpler terms : accept the null hypothesis), the p value should be > 0.05 (for 95% confidence interval). Residuals are is normal here.

### 4. Homogeneity of variance of residuals ( Homoscedasticity):

We can check it using Breusch-Pagan test ( no need to remember such names ), the null hypothesis of which is homoscedasticity.

Here too p value should be > 0.05 (for 95% confidence interval), in order to accept the null hypothesis of homoscedasticity. Model seems to be in trouble in this test.

The D-W stats value lies between 0 and 4, closer its value is to 2, better the model is.

Here value approaching to 3, is sign of some traces of auto-correlation in residual term.

### Let's go extra mile

**# Use command**

layout(matrix(c(1), 1, 1))

plot(model_2)

**# and you will get the set of 4 plots**

click to enlarge |

**The first and second plots should be random in nature with no pattern. The third one depicts the normality of error as explained above. The fourth one gives you a fair idea about presence of outliers that should be treated to improve the model.**

Enjoy reading our other articles and stay tuned with us.

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Kindly do provide your feedback in the 'Comments' Section and share as much as possible.