Simple Linear Regression with basic R

This page will show the basic R programming language of modeling Simple Linear Regression, which includes the interprets of coefficients.

Basic concepts with simple linear regression

Use pair data to find out the relationship between variables.

u is the random error, which denotes the part that Y can’t be explained by X.

Simple Linear Regression (SLR)

• x is explanatory variable, y is dependent variable
• α is the intercept，β is the slope
• β = ∂ E(y|x)/∂ x，it means when x change 1 unit, y will change β units
• α = E(y|x=0)

Population Regression Line

Given E(y|x)=α+βx

The assumption of linear regression model

1. linear in parameters

2. random sampling

3. sample variation in the explanatory variable

隨機樣本中，X_i 之值不能完全相同

4. exogeneity

給定解釋變數下，誤差項之條件期望值 = 0

5. homoskedasticity

給定解釋變數下，誤差項之條件變異數為常數

Method of Ordinary Least-Squares（OLS）

We set the model as

If we use OLS to estimate α and β ，and we denote \hat α and \hat β as OLS estimator，let residual = \hat u_i

The main goal of OLS is to get the minimum value of residual sum of squares

We can get \hat α, \hat β

Applied R in SLR model

We try to estimate the effect of education years on salary.

step 1. read data

data <- read.csv("/Users/abnerteng/Downloads/wagedata.csv") head(data)

step 2. set up the SLR model

slr <- lm(data = data, wage~educ) 
summary(slr)

step 3. Draw a scatter plot

plot(data$educ, data$wage,      
     main = 'Regression for education level and wage',      
     xlab = 'education level',      
     ylab = 'wage') 
abline(slr, col = 'blue', lwd = 2)

• the blue line is the slr model