Question

The following data give the percentage of women working in five companies in the retail and trade industry. The percentage of management jobs held by women is also shown.

% Working	67	45	73	54	61
% Management	49	21	65	47	33

1. Compute SST, SSR, and SSE.
2. Compute the coefficient of determination, r². Comment on the goodness of fit.
3. What is the value of the sample correlation coefficient?

Answer 1

Excel Megastat regression analysis output is given below.

Regression Analysis
	r²	0.724	n	5
	r	0.851	k	1
	Std. Error	10.146	Dep. Var.	Y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	811.2000	1	811.2000	7.88	.0674
Residual	308.8000	3	102.9333
Total	1,120.0000	4
Regression output					confidence interval
variables	coefficients	std. error	t (df=3)	p-value	95% lower	95% upper
Intercept	-35.0000
X1	1.3000	0.4631	2.807	.0674	-0.1737	2.7737

a)

SST = 1120

SSR = 811.20

SSE = 308.8

b)

coeff of determination = r²=0.724

72.4% of variation in dependent variable is explained by independent variable

c)

correlation coefficient = r = 0.851