An introduction to Simple Linear Regression and its applications

A method to model the relationship between two variables. Used for prediction and determining trends in data.

\[ y = \beta_0 + \beta_1x + \epsilon \] \(\beta_0\): Intercept \(\beta_1\): Slope \(\epsilon\): Error term

Minimize the sum of squared errors: \[ \sum (y_i - (\beta_0 + \beta_1x_i))^2 \]

## Loading required package: ggplot2

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## Attaching package: 'plotly'

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## `geom_smooth()` using formula = 'y ~ x'

Null Hypothesis \(H_0: \beta_1 = 0\): No linear relationship Alternative Hypothesis \(H_A: \beta_1 \neq 0\) A low p-value (< 0.05) suggests rejecting the null hypothesis.

# R code for simple linear regression
model <- lm(mpg ~ wt, data = mtcars)
summary(model)

## 
## Call:
## lm(formula = mpg ~ wt, data = mtcars)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.5432 -2.3647 -0.1252  1.4096  6.8727 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  37.2851     1.8776  19.858  < 2e-16 ***
## wt           -5.3445     0.5591  -9.559 1.29e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.046 on 30 degrees of freedom
## Multiple R-squared:  0.7528, Adjusted R-squared:  0.7446 
## F-statistic: 91.38 on 1 and 30 DF,  p-value: 1.294e-10