STAT 2 - LAB 1

Question 1

Load the Boston data set from the MASS library

Answer 1

library(MASS)
data(“Boston”)

Question 2

Retrieve description of Boston dataset

Answer 2

help(Boston)
or
?Boston

Question 3

get a glimpse of structure of data

Answer 3

str(data)
glimpse(data)
names(data)

Question 4

change int variable into factor

Answer 4

census_tracts$chas <- as.factor(census_tracts$chas)

Question 5

check levels of a factor variable

Answer 5

levels(census_tracts$chas)

Question 6

compute basic statistics for each variable

Answer 6

summary(census_tracts)

Question 7

take all numeric variables and exclude categorical ones

Answer 7

var_interest_numeric <- colnames(census_tracts)[!(colnames(census_tracts) %in% c(“chas”, “rad”))]

Question 8

plot a side-by-side histogram analysing multiple columns

Answer 8

census_tracts %>%
select(crim, zn, age) %>%
gather(cols, value) %>%
ggplot(aes(x = value)) + geom_histogram(bins = 20) + facet_wrap(.~ cols, ncol = 3)

Question 9

compute correlation between quantitative variables

Answer 9

cor(census_tracts[,var_interest_numeric]

rounded:
round(cor(census_tracts[,var_interest_numeric]), 2)

Question 10

plot the correlation matrix

Answer 10

heatmap(corr_matrix)

library(corrplot)
corrplot::corrplot(corr_matrix)
(you can plot it like this and consider the upper triangle or you can perform this before:
corr_matrix[lower.tri(corr_matrix)] <- 0 (to visualize only upper triangle))

Question 11

scatterplots of relationships between quantitative variables

Answer 11

with function pairs:

pairs(census_tracts[, c(“medv”, “lstat”,”dis”)])

Question 12

fit a simple linear regression model

Answer 12

lm.fit.simple <- lm(formula = medv ~ lstat, data = census_tracts)

Question 13

Calculate 95% confidence intervals for —0 and —1 using the function confint.

Answer 13

confint(lm.fit.simple)

Question 14

Calculate 95% confidence intervals for medv at values of lstat are 5,10,15 using the function predict.

Answer 14

predict(lm.fit.simple,
newdata = data.frame(lstat = (c(5,10,15))),
interval = “confidence”)

Question 15

Calculate 95% prediction intervals medv at values of lstat are 5,10,15 using the function predict.

Answer 15

predict(lm.fit.simple,
newdata = data.frame(lstat = (c(5,10,15))),
interval = “prediction”)

Question 16

Fit multiple linear regression model with medv as the response variable and lstat, and dis as the predictor

Answer 16

lm.fit.multiple <- lm(formula = medv ~ lstat + dis, data = census_tracts)

Question 17

compare multiple and simple linear regression model by using anova

Answer 17

anova(lm.fit.simple,lm.fit.multiple)

Question 18

Fit the multiple linear regression model with medv as the response variable, and all quantitative variables as predictors

Answer 18

lm.fit.full <- lm(formula = medv ~ . -chas -rad, data = census_tracts)