Question

Given the following pairs of data where x is the number of years of experience in a certain company and y is the annual salary:

Determine the equation of the linear regression line. Round the slope and y-intercept to the nearest integers.

Using your answer in (a), estimate the starting salary for a new hire.

Using your answer in (a), estimate the number of years (to the nearest year) an employee would have to work in the company in order to earn an annual salary of $175,000

X Y

8 70,000

10 100,000

12 115,000

13 120,000

15 120,000

16 125,000

17 130,000

18 140,000

19 145,000

20 150,000

Answer 1

X	Y	XY	X²	Y²
8	70000	560000	64	4900000000
10	100000	1000000	100	10000000000
12	115000	1380000	144	13225000000
13	120000	1560000	169	14400000000
15	120000	1800000	225	14400000000
16	125000	2000000	256	15625000000
17	130000	2210000	289	16900000000
18	140000	2520000	324	19600000000
19	145000	2755000	361	21025000000
20	150000	3000000	400	22500000000

Ʃx =	148
Ʃy =	1215000
Ʃxy =	18785000
Ʃx² =	2332
Ʃy² =	152575000000
Sample size, n =	10
x̅ = Ʃx/n = 148/10 =	14.8
y̅ = Ʃy/n = 1215000/10 =	121500
SSxx = Ʃx² - (Ʃx)²/n = 2332 - (148)²/10 =	141.6
SSyy = Ʃy² - (Ʃy)²/n = 152575000000 - (1215000)²/10 =	4952500000
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 18785000 - (148)(1215000)/10 =	803000

a)

Slope, b = SSxy/SSxx = 803000/141.6 =    5670.903955

y-intercept, a = y̅ -b* x̅ = 121500 - (5670.90395)*14.8 =    37570.62147

Regression equation :   

ŷ = 37571 + (5671) x  

b)

Predicted value of y for a new hire whose experience is 0

ŷ = 37571 + (5671) * 0 = 37571

c)

if salary = 175000 then number of years of experience =

175000 = 37571 + (5671) x

x = 24.23 = 24 years