Question

The N. Yazdak Computer Company has the following data, where y represents earnings in thousands of dollars after x years of operation.

x: 1, 3, 5, 7

y: 10, 13, 17, 22

(a) Identify your random variable(s)

(b) Plot the data (points) on graph paper

(c) Find the coefficent of correlation for the data and briefly comment on its value.

(d) Set up the necessary table to find the least squares line.

(e) Find the least square line

(f) Use your squares line from part (e) to predit earnings after 10 years.

Answer 1

a) The independent variable (x) = years of operation.

dependent variable (y) = earnings in thousands of dollars

b)

c) Coefficient of correlation

	X	Y
	1	10
	3	13
	5	17
	7	22
Total	16	62
Mean	4	15.5
SD	2.581989	5.196152

sample caovariance = 13.33

correlation coefficient = covariance / (s_x*s_y) = 13.33/(2.58*5.19) = 0.993

which says the strong positive correlation, which means increase in operation increases earnings.

d)

	X	Y	X-Mx	(X-Mx)^2	Y - My	(Y - My)^2	(X - Mx)(Y-My)
	1	10	-3	9	-1	1	3
	3	13	-1	1	2	4	-2
	5	17	1	1	6	36	6
	7	22	3	9	11	121	33
Total	16	62		Sxx = 20		Syy = 162	Sxy = 40
Mean	4	15.5
SD	2.581989	5.196152

e) y = b₀ + b₁x

b₁ = S_xy/S_xx = 4/20 = 2

b₀ = My -b₁Mx = 15.5 - 2*4 = 7.5

y =7.5 + 2x

f) for X = 10

y = 7.5 +2*10 = 27.5 thousand dollars.