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## Loading required package: ggformula
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## New to ggformula? Try the tutorials:
## learnr::run_tutorial("introduction", package = "ggformula")
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## X mpg cyl disp hp drat wt qsec vs am gear carb
## 1 Mazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4
## 2 Mazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4
## 3 Datsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1
## 4 Hornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1
## 5 Hornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2
## 6 Valiant 18.1 6 225 105 2.76 3.460 20.22 1 0 3 1
p <-ggplot(mtcars, aes(x= mpg, y=wt)) +
geom_point(color= "blue")+
stat_smooth(method = "lm",col="red")
p
fit <- lm(wt ~ mpg, data = mtcars)
summary(fit)
##
## Call:
## lm(formula = wt ~ mpg, data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.6516 -0.3490 -0.1381 0.3190 1.3684
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.04726 0.30869 19.590 < 2e-16 ***
## mpg -0.14086 0.01474 -9.559 1.29e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4945 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
par(mfrow = c(2,2))
plot(fit)
par(mfrow = c(1,1))
cor_base <- cor(x = mtcars$mpg, y = mtcars$wt)
cor_base
## [1] -0.8676594
fit <- lm(wt ~ mpg, data = mtcars) # Fit the model
summary(fit) # Report the results
##
## Call:
## lm(formula = wt ~ mpg, data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.6516 -0.3490 -0.1381 0.3190 1.3684
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.04726 0.30869 19.590 < 2e-16 ***
## mpg -0.14086 0.01474 -9.559 1.29e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4945 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
par(mfrow = c(2, 2)) # Split the plotting panel into a 2 x 2 grid
plot(fit) # Plot the model information
par(mfrow = c(1, 1)) # Return plotting panel to 1 section
cor_base <- cor(x = mtcars$mpg,y = mtcars$wt)
cor_base
## [1] -0.8676594
d <- mtcars
fit <- lm(wt ~ mpg, data = d)
d$predicted <- predict(fit)
d$residuals <- residuals(fit)
d%>% select(mpg, predicted, residuals) %>% head()
## mpg predicted residuals
## Mazda RX4 21.0 3.089154 -0.46915365
## Mazda RX4 Wag 21.0 3.089154 -0.21415365
## Datsun 710 22.8 2.835602 -0.51560210
## Hornet 4 Drive 21.4 3.032809 0.18219114
## Hornet Sportabout 18.7 3.413136 0.02686382
## Valiant 18.1 3.497653 -0.03765336
ggplot(d, aes(x= predicted, y=residuals)) +
geom_point(colors = "blue") +
geom_hline(yintercept = 0, color = "red")
## Warning: Ignoring unknown parameters: colors
d$shuffle_wt <- shuffle(d$wt)
d %>% select(wt, shuffle_wt) %>% head()
## wt shuffle_wt
## Mazda RX4 2.620 1.835
## Mazda RX4 Wag 2.875 2.875
## Datsun 710 2.320 1.935
## Hornet 4 Drive 3.215 3.730
## Hornet Sportabout 3.440 2.465
## Valiant 3.460 3.840
fit <- lm(shuffle_wt ~ mpg, data = d)
cor(x=d$mpg, y = d$shuffle_wt)
## [1] -0.3575765
ntrials <- 500
cor_i <- rep()
for(i in 1:ntrials){
cor_i[i] <- cor(x= d$mpg, y = shuffle(d$wt))
}
table (abs(cor_i) > abs(cor_base))
##
## FALSE
## 500
table (abs(cor_i) > 0.1)
##
## FALSE TRUE
## 194 306
p2 <-ggplot(mtcars, aes(x= gear, y= carb)) +
geom_point(color= "blue") +
stat_smooth(method = "lm", col="red")
p2
fit <- lm(wt ~ mpg, data = mtcars) # Fit the model
summary(fit) # Report the results
##
## Call:
## lm(formula = wt ~ mpg, data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.6516 -0.3490 -0.1381 0.3190 1.3684
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.04726 0.30869 19.590 < 2e-16 ***
## mpg -0.14086 0.01474 -9.559 1.29e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4945 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
par(mfrow = c(2, 2)) # Split the plotting panel into a 2 x 2 grid
plot(fit) # Plot the model information
par(mfrow = c(1, 1)) # Return plotting panel to 1 section
cor_base <- cor(x = mtcars$mpg,y = mtcars$wt)
cor_base
## [1] -0.8676594
ntrials <- 1000
cor_i <- rep()
for(i in 1: ntrials){
cor_i[i] <- cor(x = mtcars$gear, y =shuffle(mtcars$carb))
}