Question

3) Use the data below to answer the questions that follow

X 7 9 11 15 15 17 21 21 21 29 33 34 35 35

Y 22 20 17 17 16 12 10 10 7    4    4    3 1 0

a) Calculate the correlation coefficient “r”

b) Explain what your value for r means for this data

c) Determine the equation for the linear regression line of this data

d) What does your equation predict for an x value 17?

e) How does that compare with the actual y value for x = 17?

f) What does your equation predict for an x value of 25?

g) How accurate do you think that prediction is? Why?

Answer 1

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	7	22	49	484	154
	9	20	81	400	180
	11	17	121	289	187
	15	17	225	289	255
	15	16	225	256	240
	17	12	289	144	204
	21	10	441	100	210
	21	10	441	100	210
	21	7	441	49	147
	29	4	841	16	116
	33	4	1089	16	132
	34	3	1156	9	102
	35	1	1225	1	35
	35	0	1225	0	0
Total	303	143	7849	2153	2172

(a)

(b)

Correlation coefficient is negative and it has high magnitude 0.976 so it shows that relationship between the variables is negative and strong.

(c)

(d)

(e)

The actual of y for X=17 is 12. That is predicted value is greater than actual value.

(f)

(g)

The prediction should be near to accurate because X=25 is within range of X used to make the model.