Question

L. The following data from four manufacturing companies was collected for a regression nalysis exploring whether there is a relationship between wages and employee turnover. Average wage ($ per hourk 18 12 20 15 Turnover rate (9%) 20 40 30 a) Choose a dependent variable and an independent variable for the regression. Explain your reasoning. b) Use the regression formulas to find the best fit straight line for the data above c) According to your formula, what change in turnover rate would be associated with a $1 increase in wages? Use your forecast formula to predict the turnover rate for wages of $22 per hour. d)

Answer 1

a)
Turnover rate is dependent variable y and Average wage is independent variable x

b)

From the given data we have

X	Y	XY	X^2	Y^2
18	20	360	324	400
12	40	480	144	1600
20	6	120	400	36
15	30	450	225	900

Regression formulas are

PREDICTED Y = a b X

Detailed calcualtions are

n	4
sum(XY)	1410.00
sum(X)	65.00
sum(Y)	96.00
sum(X^2)	1093.00
sum(Y^2)	2936.00
Numerator	-600.00
Denominator	609.60
r	-0.9842
r square	0.9687
Xbar(mean)	16.2500
Ybar(mean)	24.0000
SD(X)	3.0311
SD(Y)	12.5698
b	-4.0816
a	90.3265

Hence regression equation is

ycap = 90.3265 - 4.0816x

c)

$1 increase in wage results into decrease of 4.0816% in turnover

d)

for x = 22

ycap = 90.3265 - 4.0816*22 = 0.5313