Exam-Style Question on Correlation

Ten students are given a test on calculus and a test on probability. Each test is scored out of a total of 100 marks. The scores of the students are shown in the following table:

Student	1	2	3	4	5	6	7	8	9	10
Calculus	50	68	98	90	79	78	85	99	69	59
Probability	56	74	96	90	81	80	87	98	74	66

Let \( x \) be the score on the calculus test and \( y \) be the score on the probability test.

The teacher finds that the equation of the regression line of \( y \) on \( x \) for these scores is

$$ y = 0.815x + 17.1 $$

(a) Find the value of Pearson’s product-moment correlation coefficient, \( r \).

Jaidee was absent for the calculus test and Permsak was absent for the probability test.

The teacher uses the regression line of \( y \) on \( x \) to estimate the missing scores.

Permsak scored 15 on the calculus test.

The teacher estimated his score on the probability test to be 29 to the nearest integer using the following calculation:

$$ y = 0.815(15) + 17.1 \approx 29 $$

(b) Give a reason why this method is not appropriate for Permsak.

Jaidee scored 85 on the probability test.

(c) Use an appropriate method to show that the estimated calculus test score for Jaidee is 83 to the nearest integer.