Question

22 17
19 10
30 10.5
31 11
32 15
45 6
48 11
49 5.2
68 3
65 4.2















a) Create a scatterplot of this data and comment on the relationship between the variables
b) Calculate the correlation coefficient between these two variables
c) Does a linear relationship exist?
d) Calculate the least squares regression equation
e) Using your equation, predict how long we would expect a 43 year old new hire to remain with the company

Answer 1

Here is the data:

Age	Time With Company
22	17
19	10
30	10.5
31	11
32	15
45	6
48	11
49	5.2
68	3
65	4.2

a)

b)

The provided data are shown in the table below

X	Y
22	17
19	10
30	10.5
31	11
32	15
45	6
48	11
49	5.2
68	3
65	4.2

Also, the following calculations are needed to compute the correlation coefficient:

	X	Y	X*Y	X2	Y2
	22	17	374	484	289
	19	10	190	361	100
	30	10.5	315	900	110.25
	31	11	341	961	121
	32	15	480	1024	225
	45	6	270	2025	36
	48	11	528	2304	121
	49	5.2	254.8	2401	27.04
	68	3	204	4624	9
	65	4.2	273	4225	17.64
Sum =	409	92.9	3229.8	19309	1055.93

The correlation coefficient r is computed using the following expression:

Therefore, based on this information, the sample correlation coefficient is computed as follows

c)

Yes, a negative linear relationship exists.

d)

Therefore, we find that the regression equation is:

e)

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