Use the following data to answer the questions:

Question

Correlation between y and x: r = .584

Sample size: 20



a. Find the slope and intercept, where y is the dependent variable

b. Construct an ANOVA table and indicate whether the regression is significant

c. What is the standard error of the estimate (i.e. the standard deviation of the residuals)?

Answer 1

A. First find the slope:

b = r sy

/sx = .584 * 11.695 / 4.637 = 1.473

Then find the intercept:

a = ymean - bxmean = 118.650 - 1.473 * 19.350 = 90.147



B. First find the total sum of squares:

TSS = (n-1)sy

2

= (20) * 11.6952



= 2735.461



We know that if r2



= Regression SS / Total SS:

RegSS = r2 * TSS = .5842 * 2735.461 = 932.945

Thus the Residual SS is

ResSS = TSS - RegSS = 2735.461 - 932.945 = 1802.516

From there, we divide through by 1 and n-2 respectively to get the mean squares (932.945 /

1 = 932.945; the Residual Mean Square is 1802.516 / 18 = 100.140)

Finally we find F:

F = r2

(n-2) / (1-r2) = .5842

(18) / (1 - .5842) = 9.316



We reject the null hypothesis, as 9.316 is greater than the value of F.05,1,18 = 4.41



C. The standard deviation of the residuals is the square root of the residual mean square, thus

sqrt(100.140) = 10.007.