Question

Using the following data with x as the independent variable and y as the dependent variable, answer the items.

x	-14	-22	18	8	24
y	64	253	159	9	347

у 360 Tools 324 . 288 point 1 point 2 252 216 point 3 point 4 180 144 108 point 5 72 36 0 -25 -20 -15 -10 -50 5 10 15 20 25 x b. Compute the correlation coefficient. (Round your answer to 4 decimal places.) Correlation coefficient

Answer 1

Ans : Given data with x as the independent variable and y as the dependent variable

x	y
-14	64
-22	253
18	159
8	9
24	347

Scatter plot of x versus y

400 350 347 300 253 250 200 159 150 100 64 50 9 0 -30 -20 -10 0 10 20 30 х

b) to Compute correlation coefficient between x and y

To find correlation coefficient between x and y using following formula

Σ(x – Mx)(y – My) r = Σ(x – Mx)? * Σy – My)?

x	y	(X-Mx)*(y-My)	(x-Mx)^2	(y-My)^2
-14	64	1720.32	282.24	10485.76
-22	253	-2147.68	615.04	7499.56
18	159	-112.48	231.04	54.76
8	9	-818.48	27.04	24774.76
24	347	3828.72	449.44	32616.36
14	832	2470.4	1604.8	75431.2

Mx = 2.8 , My =166.4

r = 2470.4 V1604.8 * 75431.2

r= 0..224534

correlation coefficient between x and y is 0.2245

correlation coefficient 0.2245

Ans C):

Transform the x variable by squaring each value

x	x^2	y
-14	196	64
-22	484	253
18	324	159
8	64	9
24	576	347

Scatter plot of x^2 versus y

400 350 300 250 - 200 150 100 50 0 0 100 200 300 400 500 600 700 Х2

e) Ans :

To find correlation coefficient between x^2 and y using following formula

Σ(x^2 – Mx^2)(y - My) r – Σ(x^2 – Mx^2)* * Σy – My)?

x	y	(X-Mx)*(y-My)	(x-Mx)^2	(y-My)^2
-14	64	1720.32	282.24	10485.76
-22	253	-2147.68	615.04	7499.56
18	159	-112.48	231.04	54.76
8	9	-818.48	27.04	24774.76
24	347	3828.72	449.44	32616.36
14	832	2470.4	1604.8	75431.2

r = 113398.4 172972.8 * 75431.2

r = 0.992756

correlation coefficient between x^2 and y is 0.9928

f)

Compare the correlation coefficient between x and y and X^2 and y

relationship between x and y is 0.2245

Relationship between x^2 and y is 0.9928

the Relationship between x^2 and y this is positive Relationship between X^2 and y