Question

The table below shows the number of cars sold last month by seven employees at Concord Motors and their number of years of sales experience.

Experience	Sales
1	8
2	6
2	7
4	14
5	9
6	13
8	10

Analyze this data (what is correlation coefficient, slope for regression equation, y intercept for regression equation, standard error of estimate).

Answer 1

X	Y	XY	X²	Y²
1	8	8	1	64
2	6	12	4	36
2	7	14	4	49
4	14	56	16	196
5	9	45	25	81
6	13	78	36	169
8	10	80	64	100
Ʃx =	Ʃy =	Ʃxy =	Ʃx² =	Ʃy² =
28	67	293	150	695

Sample size, n =	7
x̅ = Ʃx/n = 28/7 =	4
y̅ = Ʃy/n = 67/7 =	9.571428571
SSxx = Ʃx² - (Ʃx)²/n = 150 - (28)²/7 =	38
SSyy = Ʃy² - (Ʃy)²/n = 695 - (67)²/7 =	53.71428571
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 293 - (28)(67)/7 =	25

Correlation coefficient, r = SSxy/√(SSxx*SSyy) = 25/√(38*53.71429) = 0.5534

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Slope, b = SSxy/SSxx = 25/38 =    0.657894737

y-intercept, a = y̅ -b* x̅ = 9.57143 - (0.65789)*4 =    6.939849624

Regression equation :   

ŷ = 6.9398 + (0.6579) x  

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Sum of Square error, SSE = SSyy -SSxy²/SSxx = 53.71429 - (25)²/38 = 37.266917

Standard error of estimate, se = √(SSE/(n-2)) = √(37.266917/(7-2)) = 2.73009