4

(i) Smallest and Largest Values of the Variable ‘score’

# Find the smallest and largest values of 'score'
smallest_score <- min(econmath$score)
largest_score <- max(econmath$score)

# Print the results
cat("Smallest score:", smallest_score, "\n")

## Smallest score: 19.53

cat("Largest score:", largest_score, "\n")

## Largest score: 98.44

(ii) Assumption MLR.6 and Testing Ho: β₁ = 0

(iii) Estimating the Model and Testing Ho: β₁ = 0

# Fit the linear model
model <- lm(score ~ colgpa + acteng, data = econmath)

# Calculate the t-statistic and its associated p-value for testing Ho: β₁ = 0
t_statistic <- summary(model)$coefficients["colgpa", "t value"]
p_value <- summary(model)$coefficients["colgpa", "Pr(>|t|)"]

t_statistic

## [1] 18.51467

p_value

## [1] 4.213677e-64