Question

Calculate Pearson’s r and the coefficient of determination from the following data. Summarize your findings in a sentence that interprets both r and r².

Name	Test 1	Test 2
Sheldon	1	3
Leonard	4	6
Rajesh	7	7
Howard	3	5
Penny	6	4
Amy	2	4
Bernadette	5	6

Answer 1

We have to find Pearson’s r and the coefficient of determination.

Formula is:

n = 7

	x	y	xy	x^2	y^2
	1	3	3	1	9
	4	6	24	16	36
	7	7	49	49	49
	3	5	15	9	25
	6	4	24	36	16
	2	4	8	4	16
	5	6	30	25	36
Total	28	35	153	140	187

Coefficient of determination is:

Interpretation of Pearson r :

There is a positive correlation between test1 and test2.

Interpretation of the coefficient of determination:

50.30% variation explained by the model using regressor.