Simple Linear Regression is a statistical method used to model the relationship between two variables: a dependent variable and an independent variable. The goal is to find the line of best fit that represents the relationship between the two variables. This guide will cover the basics of simple linear regression and how it can be used in data analysis.

The slope of the line of best fit can be interpreted as the rate of change of the dependent variable for every one unit change in the independent variable. The y-intercept represents the predicted value of the dependent variable when the independent variable is . The coefficient of determination (R-squared) measures the proportion of variance in the dependent variable that is explained by the independent variable.

The equation for simple linear regression is: \[ y = mx + b \] Where ‘y’ is the dependent variable, ‘m’ is the slope of the line and ‘b’ is the y-intercept.

The slope, ‘m’, tells us how much the dependent variable changes for every one unit change in the independent variable. \[ \dfrac{dy}{dx} = m \] The y-intercept, ‘b’, tells us the value of the dependent variable when the independent variable is 0. \[ y(0) = b \]

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## Call:
## lm(formula = Exam_Score ~ Hours_Studied, data = data)
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## Residuals:
##      Min       1Q   Median       3Q      Max 
## -24.6443  -4.8623  -0.2705   4.9405  20.2559 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    53.2301     7.2184   7.374 1.97e-09 ***
## Hours_Studied   2.9298     0.2821  10.385 7.25e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.142 on 48 degrees of freedom
## Multiple R-squared:  0.692,  Adjusted R-squared:  0.6856 
## F-statistic: 107.8 on 1 and 48 DF,  p-value: 7.25e-14

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summary(cars)

##      speed           dist       
##  Min.   : 4.0   Min.   :  2.00  
##  1st Qu.:12.0   1st Qu.: 26.00  
##  Median :15.0   Median : 36.00  
##  Mean   :15.4   Mean   : 42.98  
##  3rd Qu.:19.0   3rd Qu.: 56.00  
##  Max.   :25.0   Max.   :120.00