if (!require(AER)) install.packages("AER")
## Loading required package: AER
## Loading required package: car
## Loading required package: carData
## Loading required package: lmtest
## Loading required package: zoo
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
## Loading required package: sandwich
## Loading required package: survival
library(AER)
data("Affairs", package = "AER")
head(Affairs)
## affairs gender age yearsmarried children religiousness education occupation
## 4 0 male 37 10.00 no 3 18 7
## 5 0 female 27 4.00 no 4 14 6
## 11 0 female 32 15.00 yes 1 12 1
## 16 0 male 57 15.00 yes 5 18 6
## 23 0 male 22 0.75 no 2 17 6
## 29 0 female 32 1.50 no 2 17 5
## rating
## 4 4
## 5 4
## 11 4
## 16 5
## 23 3
## 29 5
summary(Affairs)
## affairs gender age yearsmarried children
## Min. : 0.000 female:315 Min. :17.50 Min. : 0.125 no :171
## 1st Qu.: 0.000 male :286 1st Qu.:27.00 1st Qu.: 4.000 yes:430
## Median : 0.000 Median :32.00 Median : 7.000
## Mean : 1.456 Mean :32.49 Mean : 8.178
## 3rd Qu.: 0.000 3rd Qu.:37.00 3rd Qu.:15.000
## Max. :12.000 Max. :57.00 Max. :15.000
## religiousness education occupation rating
## Min. :1.000 Min. : 9.00 Min. :1.000 Min. :1.000
## 1st Qu.:2.000 1st Qu.:14.00 1st Qu.:3.000 1st Qu.:3.000
## Median :3.000 Median :16.00 Median :5.000 Median :4.000
## Mean :3.116 Mean :16.17 Mean :4.195 Mean :3.932
## 3rd Qu.:4.000 3rd Qu.:18.00 3rd Qu.:6.000 3rd Qu.:5.000
## Max. :5.000 Max. :20.00 Max. :7.000 Max. :5.000
data("mtcars")
head(mtcars)
## mpg cyl disp hp drat wt qsec vs am gear carb
## Mazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4
## Mazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4
## Datsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1
## Hornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1
## Hornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2
## Valiant 18.1 6 225 105 2.76 3.460 20.22 1 0 3 1
summary(mtcars)
## mpg cyl disp hp
## Min. :10.40 Min. :4.000 Min. : 71.1 Min. : 52.0
## 1st Qu.:15.43 1st Qu.:4.000 1st Qu.:120.8 1st Qu.: 96.5
## Median :19.20 Median :6.000 Median :196.3 Median :123.0
## Mean :20.09 Mean :6.188 Mean :230.7 Mean :146.7
## 3rd Qu.:22.80 3rd Qu.:8.000 3rd Qu.:326.0 3rd Qu.:180.0
## Max. :33.90 Max. :8.000 Max. :472.0 Max. :335.0
## drat wt qsec vs
## Min. :2.760 Min. :1.513 Min. :14.50 Min. :0.0000
## 1st Qu.:3.080 1st Qu.:2.581 1st Qu.:16.89 1st Qu.:0.0000
## Median :3.695 Median :3.325 Median :17.71 Median :0.0000
## Mean :3.597 Mean :3.217 Mean :17.85 Mean :0.4375
## 3rd Qu.:3.920 3rd Qu.:3.610 3rd Qu.:18.90 3rd Qu.:1.0000
## Max. :4.930 Max. :5.424 Max. :22.90 Max. :1.0000
## am gear carb
## Min. :0.0000 Min. :3.000 Min. :1.000
## 1st Qu.:0.0000 1st Qu.:3.000 1st Qu.:2.000
## Median :0.0000 Median :4.000 Median :2.000
## Mean :0.4062 Mean :3.688 Mean :2.812
## 3rd Qu.:1.0000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :1.0000 Max. :5.000 Max. :8.000
# mtcars Description: The mtcars dataset comprises 32 observations on 11 variables, detailing aspects like miles per gallon (MPG), number of cylinders, horsepower, and weight for various car models. This dataset provides insights into how different design choices impact vehicle performance.
# Affairs Description: The Affairs dataset includes information on extramarital affairs, rating of marriage, age, years married, and other demographic factors for a sample of individuals. It offers a glimpse into personal and social factors associated with marital satisfaction and infidelity.
library(ggplot2)
ggplot(mtcars, aes(x = hp, y = mpg)) +
geom_point() +
labs(title = "MPG vs Horsepower",
x = "Horsepower",
y = "Miles per Gallon") +
theme_minimal()
ggplot(Affairs, aes(x = rating, y = affairs)) +
geom_jitter(width = 0.2, height = 0.2, alpha = 0.5) +
labs(title = "Marriage Rating vs Number of Affairs",
x = "Marriage Rating",
y = "Number of Affairs") +
theme_minimal()
# mtcars: This is a cross-sectional dataset because it captures data at a single point in time, showing the relationship between car specifications and their performance.
# Affairs: This dataset can be considered cross-sectional as well, since it collects information about individuals' marital satisfaction and incidents of affairs at one point in time.
# Covariance is a measure that indicates the extent to which two variables change together. If the value is positive, it means the variables tend to move in the same direction, whereas a negative value indicates they move in opposite directions.
# Variance quantifies the variation of a dataset from its mean, essentially describing the spread of the data points.
# The slope coefficient in a simple linear regression, calculated as Cov(y,x)/Var(x), quantifies the average change in the dependent variable for a one-unit change in the independent variable. This works because dividing the covariance by the variance of x normalizes the relationship between x and y, thereby quantifying the direct influence of x on y in linear terms.
x <- mtcars$mpg
y <- mtcars$hp
cov_yx <- cov(y, x)
var_x <- var(x)
slope_formula <- cov_yx / var_x
model <- lm(y ~ x)
slope_regression <- coef(model)[2]
print(paste(slope_formula))
## [1] "-8.82973099206822"
print(paste(slope_regression))
## [1] "-8.82973099206822"