Question

Linear regression is a statistical tool commonly used to find a relationship that exists between a variable and one explanatory variable. What are the factors that affect a linear regression model? How can you accomplish linear regression in R? Please provide an example to illustrate your assertions.

Answer 1

First you need to check assumptions of linear regression model.

There are four assumptions associated with a linear regression model:

1. Linearity: The relationship between X and the mean of Y is linear.
2. Homoscedasticity: The variance of residual is the same for any value of X.
3. Independence: Observations are independent of each other.
4. Normality: For any fixed value of X, Y is normally distributed.

This can be done by using four in one plot in R.

Also it is important to check presence of outliers.

Example using R:

step 1. Import data in R

step 2. Fit regression model using lm() function.

step 3. Plot that fitted model to get four in one plot.

Example:

Consider an example of predicting weight of person using its height as predictor variable.

> height = c(151, 174, 138, 186, 128, 136, 179, 163, 152, 131)

> weight = c(63, 81, 56, 91, 47, 57, 76, 72, 62, 48)
> fit=lm(weight~height)
> summary(fit)

Call:
lm(formula = weight ~ height)

Residuals:
Min 1Q Median 3Q Max
-6.3002 -1.6629 0.0412 1.8944 3.9775

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -38.45509 8.04901 -4.778 0.00139 **
height 0.67461 0.05191 12.997 1.16e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.253 on 8 degrees of freedom
Multiple R-squared: 0.9548, Adjusted R-squared: 0.9491
F-statistic: 168.9 on 1 and 8 DF, p-value: 1.164e-06

> par(mfrow=c(2,2))# it divides graph window in 4 sections
> plot(fit)