NOTATIONS USED IN THIS COURSE
SIMPLE LINEAR REGRESSION
1) Population regression model: Yi = B1 + B2 Xi + ui
where,
B1 and B2 are parameters or regression coefficients
ui is the error term or noise component
Y is explained or dependent variable
X is independent or explanatory variable
2) Sample regression model: Yi = b1 + b2 Xi + ei
where,
b1 is the estimator of B1
b2 is the estimator of B2
ei is the residual term (It is analogous to ui and can be regarded as its estimator)
Y is explained or dependent variable
X is independent or explanatory variable
3) Yi : Actual Yi
𝑌̂i : Predicted Yi
4) xi = Xi - 𝑋̅
x is the deviation of X variable from it’s mean.
We know that, Ʃ (Xi - 𝑋̅ ) = 0 i.e. sum of deviations from mean is always equal to zero. This implies
that Ʃ xi = 0
5) 2 : Variance of the disturbance term ui
MULTIPLE LINEAR REGRESSION (THREE VARIABLES MODEL)
1) Population regression model: Yi = B1 + B2 X2i + B3 X3i + ui
where,
B1,B2 and B3 are parameters or regression coefficients
ui is the error term or noise component
Y is explained or dependent variable
X2 and X3 are independent or explanatory variables
2) Sample regression model: Yi = b1 + b2 X2i + b3 X3i + ei
where,
b1 is the estimator of B1
b2 is the estimator of B2
b3 is the estimator of B3
ei is the residual term (It is analogous to ui and can be regarded as its estimator)
Y is explained or dependent variable
X2 and X3 are independent or explanatory variables
3) x2i = X2i - 𝑋̅ 2
x2 is the deviation of X2 variable from it’s mean.
We know that, Ʃ (X2i - 𝑋̅ 2) = 0 i.e. sum of deviations from mean is always equal to zero.
This implies that Ʃ x2i = 0
X3i = X3i - 𝑋̅ 3
x3 is the deviation of X3 variable from it’s mean.
We know that, Ʃ (X3i - 𝑋̅ 3) = 0 i.e. sum of deviations from mean is always equal to zero.
This implies that Ʃ x3i = 0
4) Yi : Actual Yi
𝑌̂i : Predicted Yi
5) 2 : Variance of the disturbance term ui