Question:

A target variable y is known to depend linearly on 12 predictor variables, x1, x2,.., x12.

20 experiments are performed to determine the regression coefficients. In each experiment, the values of the predictor variables and the target variable are measured. The following is the summary of the experiments. \(S{{S}_{Total}}\) = 44157; \(S{{S}_{Error}}\) = 3479

What is the number of degrees of freedom of

1. \(S{{S}_{Total}}\)
2. \(S{{S}_{Error}}\)
3. \(S{{S}_{\text{Regression}}}\)
4. Compute the statistic that you would use to determine if the regression is significant.
5. What distribution describes the statistic you computed above?
6. Compute R ² and R ² adj
7. Is the regression significant?

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