# 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: 19.53cat("Largest score:", largest_score, "\n")## Largest score: 98.44In multiple linear regression (MLR), assumption MLR.6 addresses the error term’s normality. The error term may not always have a perfect normal distribution in real-world situations. This could be due to various factors and may lead to issues with using the usual t-statistic to test Ho: β₁ = 0. One of the main presumptions of linear regression, the normality of errors, is violated if Assumption MLR.6 is not true for the error term “u.” Consequently, the standard t-statistic might not fit a t-distribution, and the p-value that goes along with it might not have the desired characteristics. ## (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] 18.51467p_value## [1] 4.213677e-64