Construct an ANOVA table and indicate whether the regression is significant

Use the following data to answer the question.







Correlation between y and x: r = .584

Sample size: 20


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

Environmental & Atmospheric Sciences

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