midterm formulae Flashcards
Independent variable is endogenous if
Correlated with the error term
-
Average
Predicted
B1^
Sum (x1-x-)(y1-y-) / sum (x1 - x-)^2
B0^
Y- - B1^x-
Ssr
Sum u1- squared
SST
Sum (y1 minus yhat)squared
R squared
Variation in y explained by the variables in this model
1 - ssr/sst
Mpc ^
Slope
Apc^
Cons^ / income
B0/income. + b1
B1log(sale)
B1 means
Elasticity of y with respect to sales
A 1% increase in sales increase y by b1
Y
Dependent variable
X
Independent variable
U
Error term / unobserved factors
B0
Intercept value of y when x = 0
B1
Slope / effect of x on y
Y will (+-) by b1 for every x
N
Sample size
Omitted variable
Variable the omitting of would cause a negative bias
For wrong sign
Need a positive variable with negative correlation
Or
Need a negative variable with positive correlation
Diff in y
B1(triangle) + b2(triangle)
Triangles = difference veteran ppl A and B
Log log
Log y = b1 log x
B1 is percentage change in y when x changes by 1%
Level log
B1log x
B1/100 is change in y per percentage change in x
Log level
Log y
B1 is percentage change in y when x changes by 1 unit
Billionare = 0.195log (Pop)
A 1% Increase in pop means 0.195 increase in billionaires
Change in siblings
1=0.94changesibs
Residuals u1^
Y1 - y1^
Diff between actual and predicted values
Ols
Estimates the relationship between variables while minimising residual errors.
E(points|attempts) = b0 + b1attempts
The average of points in the population lies on the straight line described by b0 + b1atttwmpts.
Mean
Average
Omitting variables (x2, x3)
Causes bias in the estimation of b1
The bias depends on
The correlation between x1 and the omitted variables
The size of the coefficients b1 (large partial efffects mean larger bias)
If x1 is highly correlated with x2, omitting them leads to
A significant change in the estimates coefficient of x1.
B1(squiggly line) from simple regressions and b1^ can be
Very different due to the omitted variable bias
The more correlates x1 is with x2 and x3,
The larger the effects fo x2 and x3 on y are, the greater difference between b1 squiggle and b1^
B1 squaggle
B1^ + b2^music note 1 squiggle
