Can someone please explain how in the example below will we conduct an ANOVA test to test whether or not a linear relationship exists: (These are just some values that I entered randomly.) \(X\) : 23 34 45 24 23 12 23 44 18 23 \(Y\) : 45 23 78 90 36 67 78 12 55 11 I have calculated the following values required for Linear Regression : \(\bar X = 26.9;\ \bar Y=49.5\) \(S_{xx}\) = 1040.9; \(S_{yy}\) = 7394.5; \(S_{xy}\) = -631.5 \(\hat\alpha\) = 65.8199; \(\hat\beta\) = -0.6067 I also conducted a t-test for the beta value: \(H_{0}: \beta = 0 \) \(H_{1}: \beta \neq 0\) \(t = -0.661\) From Tables, Critical Value = \(-2.306\) So, we do not have sufficient evidence to reject H0 at the 5% level. So, it is reasonable to conclude that true value of beta is zero, ie, there is no linear relationship. For the ANOVA test, what will be the treatments and the dummy variables? Also how are we going to calculate \(SS_{R}\) and \(SS_{B}\)?
Isnt Anova used to test if the means are the same? So Anova would test if X-bar and Y-bar are the same.
Yes, I know that ANOVA is used to test if the treatment means are equal to the overall mean. However, the Course Notes state that (on page 26 of Chapter 14: Analysis of Variance): Moreover, when I used Excel's Data Analysis add-on to do a linear regression, the final results also had information about an ANOVA test. However, I was unable to understand how these values were calculated. Here is a screenshot of the Excel page. I am also attaching the Excel file with this message for a ready reference. P.S: I have compressed the Excel file as we can't upload .xlsx files.
Have you tried changing the X values to 0's and 1's and then seeing if the R^2 (from regression analysis) is equal to SS_Regression/SS_Total from your ANOVA table above?
Satya is on the righ track. Also question 12 from September 2009 gives an idea of the relationship between anova and regression. Specifically the questions asked in section (ii).
