Multiple regression analysis: Estimation and assumptions
4 important questions on Multiple regression analysis: Estimation and assumptions
Explain the concept of matrix symmetry
If you have a square matrix, the transposed of the matrix must be equal to the original matrix.
So with transpose, we turn columns into rows.
We can then compare the original row with this 'new' row (that used to be a column.
If they are equal (for all rows and columns) you have symmetry.
What do the individual components of a multiple regression model in matrix form look like?
Explain the first 2 measures of fit; what they are and how they differ
2. RMSE
Similarity
Both look at the spread (of the observed Y's ) around the regression line, so; how well does our model fit the observed data.
Difference
SER has a Degrees of Freedom correction (including the number of regressors, k, in the denominator),
RMSE does not have a correction
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Both SER and RMSE look at the spread of the observed data around the regression line, can you explain how they do that
Note;
Y - Y-hat = u-hat.
So they square these u-hats, sum them, and then take the average of that.
By taking the square root and the end, they undo the squaring and now the values are expressed in terms of the same units as the data again.
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