Let’s take a look at simple linear regression in statistics.

We’ll cover: What is it, Mathematical Representations, and some examples with car road test data from the 70s.

Simple Linear Regression is a statistical method that allows us to summarize and study relationships between two continuous (quantitative) variables.

In its simplest form, the model for simple linear regression is:

\[ Y = \beta_0 + \beta_1X + \epsilon \]

Where: - \(Y\) is the dependent variable - \(X\) is the independent variable - \(\beta_0\) is the intercept - \(\beta_1\) is the slope - \(\epsilon\) is the error term

We’ll use the mtcars dataset for our example.

## 
## 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

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

## 
## Attaching package: 'plotly'

## The following object is masked from 'package:ggplot2':
## 
##     last_plot

## The following object is masked from 'package:stats':
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##     filter

## The following object is masked from 'package:graphics':
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##     layout

Simple Linear Regression is a fundamental tool in statistical analysis that helps in understanding the relationship between two continuous variables.