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x 35 45 52 66 76 81 y 1 4 10 20 26 39 A. Determine the Correlation Coefficient f

ID: 3316584 • Letter: X

Question

                     

x

35

45

52

66

76

81

y

1

4

10

20

26

39

A. Determine the Correlation Coefficient for the above ordered paired data set.

B.Determine the Coefficient of Determination.

C.How much of the relationship or association between x and y is due to random chance?

D.Use Linear Regression method to create a Linear Equation for this data.

E.Using your derived equation, what would be the expected value of y if x is equal to 65?

Using your derived equation, what would be the expected value of y if x is equal to 65?

x

35

45

52

66

76

81

y

1

4

10

20

26

39

Explanation / Answer

Ans:

slope,b=(6*7190-355*100)/(6*22647-355^2)=0.775

y-intercept,a=(100-0.775084*355)/6=-29.192

A)correlation,cof.,r=(6*7190-355*100)/SQRT((6*22647-355^2)*(6*2714-100^2))=0.971

B)Cofficient of determination,r2=0.971^2=0.942

C)1-r^2=1-0.942=0.058,5.8% variation is due to chance.

94.2% is dur to linear variation.

D)y'=0.775x-29.192

when x=65

y'=0.775*65-29.192=21.183

x y xy x^2 y^2 1 35 1 35 1225 1 2 45 4 180 2025 16 3 52 10 520 2704 100 4 66 20 1320 4356 400 5 76 26 1976 5776 676 6 81 39 3159 6561 1521 Total= 355 100 7190 22647 2714 slope,b= 0.775084 y-intercept,a= -29.1925 r= 0.97074