Question

A teacher wishes to investigate if there is any relationship between a student’s exam score in Mathematics (X) and the exam score in Accounting (Y). A sample of 11 students is randomly selected and the results are summarized in the ANOVA table below:
                                                                                                                   15 Marks
df SS
Regression 1 1305.68
Residual 9 81.96
Total 10 1387.64

Coefficients Standard Error t Stat p-value
Intercept 24.13 4.657 5.182 0.005
MathScore 0.759 0.063 11.974 0.001
a. What is the estimated regression equation that relates the exam score in accounting (Y) to the score in mathematics (X)?
b. What is the estimated exam score in accounting if a student got a score of 80 in mathematics?
c. Is the regression relationship significant? Use the p-value approach and 3% level of significance.
d. Compute the coefficient of determination between the exam score in accounting and the exam score in mathematics. Interpret the result in the context of the problem.

Answer 1

(a) The estimated regression equation is:

y = 24.13 + 0.759*x

(b) Put x = 80

y = 24.13 + 0.759*80

y = 84.85

(c) The hypothesis being tested is:

H₀: β₁ = 0

H₁: β₁ ≠ 0

The p-value from the output is 0.001.

Since the p-value (0.001) is less than the significance level (0.03), we can reject the null hypothesis.

Therefore, we can conclude that the regression relationship is significant.

(d) The coefficient of determination between the exam score in accounting and the exam score in mathematics is 1305.68/1387.64 = 0.941.

94.1% of the variability in exam scores in accounting is explained by the exam score in mathematics.