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
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