Question

Calculate the sample correlation and covariance for (i) Final_exam and assignment_grade; (ii) Final_exam and Tutorial_attend; and (iii) assignment_grade and Tutorial_ attend. Once again using Excel formulae without the use of Data Analysis Tool Pack very important the teacher wants us to use hand by hand using excel in a step by step manner: e.g. calculating the sample mean which would be sum (x) /n...

we can't use excel formula that is (=covariance(A..)

please show steps with snipping tool.

Final_exam	assignment_grade	Tutorial_attend
100	90	5
100	75	5
90	75	5
85	85	5
85	100	5
80	95	5
70	80	5
60	95	5
60	80	5
55	95	5
55	25	4
50	80	5
45	90	5
40	65	5
40	65	4
35	0	3
30	70	4
30	55	4
25	85	5
25	90	4
15	5	3
15	80	5
15	50	5
15	45	3
5	75	3
5	70	4
100	100	5
95	75	5
90	100	5
85	85	5
80	95	5
70	45	5
70	100	5
65	90	5
60	100	5
55	65	4
55	90	5
55	80	4
50	50	5
45	50	4
45	75	3
40	75	5
40	70	5
35	90	4
30	95	5
30	55	5
25	75	4
25	20	3
25	65	2
15	60	4
15	60	4
15	80	5
10	55	4
10	80	2
0	0	2

Answer 1

a)

Final_exam   assignment_grade

sample size ,	n    =	55
here,   x̅   = Σx / n=	46.64	,	ȳ = Σy/n =	70.91

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	2565	3900	43402.72727	33504.5	17993.18
mean	46.64	70.91	SSxx	SSyy	SSxy

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.4718

covariance=Σ(x-x̅)(y-ȳ) / (n-1) =   17993.1818/54=   333.207

.........................

Final_exam Tutorial_attend

sample size ,	n    =	55
here,   x̅   = Σx / n=	46.64	,	ȳ = Σy/n =	4.36

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	2565	240	43402.72727	42.7	807.27
mean	46.64	4.36	SSxx	SSyy	SSxy

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.5928
covariance=Σ(x-x̅)(y-ȳ) / (n-1) =   807.2727/54=   14.9495

................

assignment_grade   Tutorial_attend

sample size ,	n    =	55
here,   x̅   = Σx / n=	70.91	,	ȳ = Σy/n =	4.36

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	3900	240	33504.54545	42.7	696.82
mean	70.91	4.36	SSxx	SSyy	SSxy

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.5824
covariance=Σ(x-x̅)(y-ȳ) / (n-1) =   696.8182/54=   12.904

....................

THANKS

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