# Load the wooldridge library
library(wooldridge)
# Load the econmath dataset
data("econmath")
# (i) Logical Range of "score" Variable:
# The "score" variable represents a score, and logically, its smallest value in theory is typically 0.
# The largest value depends on the upper limit of the score scale.
# Find the smallest and largest values in the sample for the "score" variable
min_score <- min(econmath$score)
max_score <- max(econmath$score)
min_score
## [1] 19.53
max_score
## [1] 98.44
# (ii) Assumption MLR.6 and Testing H0: B3 = 0:
# Assumption MLR.6 states that the error term u should have a mean of zero.
# In this case, Assumption MLR.6 cannot hold for the error term u because the "score" variable is likely bounded within a specific range.
# (iii) Estimate the Model and Obtain the t-Statistic and p-value:
# Estimate the model
model <- lm(score ~ colgpa + actmth + acteng, data = econmath)
# Obtain the t-statistic and p-value for testing H0: B3 = 0
t_statistic <- summary(model)$coefficients["acteng", "t value"]
p_value <- summary(model)$coefficients["acteng", "Pr(>|t|)"]
t_statistic
## [1] 0.4660776
p_value
## [1] 0.6412852
# The p-value is a measure of the evidence against the null hypothesis (H0: B3 = 0) based on the available data.
# While the assumption of normality of the error term is important for the validity of the t-statistic, violations of this assumption don't necessarily make the p-value untrustworthy.
# It means that the t-statistic may not follow the standard t-distribution, but it doesn't invalidate the evidence provided by the p-value.
# It's essential to acknowledge the assumption violation and interpret the results cautiously.