Question

Exercise 4 (Chapter 11.3) A corporation administers an aptitude test to all new sales representatives. Management is interested in the extent to which this test is able to predict sales representatives' eventual success. The accompanying table records average weekly sales (in thousands of dollars) and aptitude test scores for a random sample of ten representatives. Sales | 12 Score 53 13 60 28 86 24 75 19 80 17 85 14 64 13 60 20 67 16 63 (a) Estimate the linear regression of weekly sales on aptitude test scores. (b) Interpret the estimated slope of the regression line.

Answer 1

(a)

x	y	(x - xbar)	(y - ybar)	(x - xbar)*(y - ybar)	(x - xbar)²	(y - ybar)²
12	53	-5.60	-16.30	91.28	31.36	265.69
13	60	-4.60	-9.30	42.78	21.16	86.49
28	86	10.40	16.70	173.68	108.16	278.89
24	75	6.40	5.70	36.48	40.96	32.49
19	80	1.40	10.70	14.98	1.96	114.49
17	85	-0.60	15.70	-9.42	0.36	246.49
14	64	-3.60	-5.30	19.08	12.96	28.09
13	60	-4.60	-9.30	42.78	21.16	86.49
20	67	2.40	-2.30	-5.52	5.76	5.29
16	63	-1.60	-6.30	10.08	2.56	39.69
xbar (average)	ybar (average)	Σ(x - xbar)	Σ(y - ybar)	Σ(x - xbar)*(y - ybar)	Σ(x - xbar)²	Σ(y - ybar)²
17.60	69.30	0	0	416	246	1184
b1 = Σ(x - xbar)*(y - ybar)/Σ(x - xbar)²	1.69
bo = ybar - b1*xbar	39.57

The regression model is:

y = 39.57 + 1.69*x

(b) For every additional sales, score will increase by 1.69.

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