Question

2. A psychology professor tried to determine if midtest grades were correlated with last test grades. To do this he selected a sample of 10 students and recorded the two grades for each student. Those grades appear below.  

            Midtest 85      90     72     75     82     95     80      83     81     95

last test 83      91    75     85     65     92      83      86    79     98

            a) Compute a Pearson's r correlation for these grades.

            b) Evaluate this outcome.

            c) Discuss the strength of this relationship.

Answer 1

Midtest (X)	last test (Y)	X^2	Y^2	XY
85	83	7225	6889	7055
90	91	8100	8281	8190
72	75	5184	5625	5400
75	85	5625	7225	6375
82	65	6724	4225	5330
95	92	9025	8464	8740
80	83	6400	6889	6640
83	86	6889	7396	7138
81	79	6561	6241	6399
95	98	9025	9604	9310
838	837	70758	70839	70577

r = 0.6755

b) Evaluate this outcome.

As the correlation is 0.6755 which means the Midtest and last are positively correlated, as if a student has more marks in Midtest then there is high chance he will have more marks in last test

c) Discuss the strength of this relationship.

As the correlation is between 0.3 and 0.7

this moderately positive correlation