Use the following information to answer questions a-d. Two methods were compared

Question

Use the following information to answer questions a-d. Two methods were compared using 50 duplicate samples ( n = 100) for linear regression analysis. The data are as follows:

Sum of Method A ( reference)           = 400

Sum of Method B ( test)                     = 450

Mean of Method A                             = 9

Mean of Method B                             = 11

Sum of (method A)2                                    = 5000

Sum of ( Method B)2                          = 5500

Sum of xy                                           = 4500

a. What is the slope of the regression line?

b. What is the y intercept of the regression line?

c. How is the standard error of the estimate calculated? List the formula.

d. What is the correlation coefficient of the regression line, of the above question b.

Explanation / Answer

Ans:

Regression Equation(y) = a + bx

Slope(b) = (NXY - (X)(Y)) / (NX2 - (X)2)

Intercept(a) = (Y - b(X)) / N

a)Method A(x)

Method B(y)

slope,b=(100*4500-400*450)/(100*5000-400^2)=0.794

b)

y-intercept=(450-0.794*400)/100=1.324

c)

Standard error estimate=sqrt((perdicted value-actual value)^2/n)

d)

Correlation cofficient=(100*4500-400*450)/SQRT((100*5000-400^2)*(100*5500-450^2))=0.786

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