title: “Simple Linear Regression” output: isoslides_presentation

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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

head(mtcars[, c("mpg", "wt")])

##                    mpg    wt
## Mazda RX4         21.0 2.620
## Mazda RX4 Wag     21.0 2.875
## Datsun 710        22.8 2.320
## Hornet 4 Drive    21.4 3.215
## Hornet Sportabout 18.7 3.440
## Valiant           18.1 3.460

summary(mtcars[, c("mpg", "wt")])

##       mpg              wt       
##  Min.   :10.40   Min.   :1.513  
##  1st Qu.:15.43   1st Qu.:2.581  
##  Median :19.20   Median :3.325  
##  Mean   :20.09   Mean   :3.217  
##  3rd Qu.:22.80   3rd Qu.:3.610  
##  Max.   :33.90   Max.   :5.424

ggplot(mtcars, aes(x = wt, y = mpg)) +
geom_point() +
labs(
title = "Scatterplot of MPG vs Weight",
x = "Weight (1000 lbs)",
y = "Miles per Gallon"
)

lm_fit <- lm(mpg ~ wt, data = mtcars)
summary(lm_fit)

## 
## 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

ggplot(mtcars, aes(x = wt, y = mpg)) +
geom_point() +
geom_smooth(method = "lm", se = FALSE, color = "red") +
labs(
title = "Linear Regression of MPG on Weight",
x = "Weight (1000 lbs)",
y = "Miles per Gallon"
)

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

plot_ly(
data = mtcars,
x = ~wt,
y = ~hp,
z = ~mpg,
type = "scatter3d",
mode = "markers"
) %>%
layout(
title = "3D Plot of MPG vs Weight and Horsepower",
scene = list(
xaxis = list(title = "Weight"),
yaxis = list(title = "Horsepower"),
zaxis = list(title = "MPG")
)
)

mtcars$residuals <- resid(lm_fit)
mtcars$fitted    <- fitted(lm_fit)

ggplot(mtcars, aes(x = fitted, y = residuals)) +
geom_hline(yintercept = 0, linetype = "dashed") +
geom_point() +
labs(
title = "Residuals vs Fitted Values",
x = "Fitted MPG",
y = "Residuals"
)

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