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Assume that you have a dataset with a predictor (feature) X and the target Y ....

Assume that you have a dataset with a predictor (feature) X and the target Y . You run simple linear regression (Y ∼ X) and get the best fit with RSS = 20 and TSS = 120?

1. What is the covariance between X and Y if the variances of X and Y are Var(X) = 15 and Var(Y ) = 20.
2. Repeat if RSS = 50 and TSS = 40. Discuss the result.

Math   Statistics-And-Probability   
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Answer #1

a) We first compute the correlation coefficient here as:

Therefore the covariance here is computed as:

Therefore 15.8119 is the required covariance between X and Y here.

2) The given RSS and TSS value combination is not possible here. This is because the residual sum of squares cannot be less than the total sum of squares. Therefore the given set of values are not possible here.

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