Regression residuals:
Minimize sum of squared regression residuals:
Ordinary Least Squares (OLS) estimates:
Fitted values and residuals:
Algebraic properties of OLS regression:
Measures of Variation:
1) Total sum pf squares (total car in Y):
2) Explained sum of squares (var explained by regression):
3) Residual sum of squares (car not exp by regression):
Decomposition of total variation:
Goodness-of-Fit measures:
R-squared interpretation: fraction of the total variation in Y explained by the regression
Lin-Lin: change by $𝛽1
Log-Lin: change by 𝛽1(%)
Log-Log: change by 𝛽1 %
Change scale of Y by constant k: multiply all coefficient estimate by k
Change X by a multiplicative constant k, leave Y alone: if multiply X by k, then the slope coefficient change by
multiplying 1/k, no impact on intercept
Homoskedasticity:
The value of Y must contain no info about variability of error term
Variance of the OLS estimators:
Estimating error variance:
Standard errors (how precisely the regression coefficients are estimated) for regression coefficients:
OLS est of multiple regression model:
1) Regression residuals:
2) Min sum of squared residuals:
MLR – Algebraic properties of OLS regression:
MLR – Decomposition of total variation:
1) R-squared:
2) Alternative expression for R-squared: