Econ123a mid1 review
E(x)=x*f(x)
E[ax] = aE[x]
E[x + b] = E[x] + b
E[ax + b] = aE[x] + b
E[ x ] = ux
Variance:E[(x – E(x))2] = E[(x – ux)2] = σ2x =E[x2] –ux 2
Var(x)=
*f(x)
standard deviation of variance (σx)
simple linear regression model
V[ax] = a2V[x]
V[x + b] = V[x]
V[ax + b] = a2V[x]
mean (u)
normally distributed:Y~ N(u, σ2)
Y~N(10,9). What is Prob(Y≤16)?
Prob[Z≤(16-u)/σ] = Prob[Z≤(16-10)/3] =
Population regression function (PFR)
Φ(2)=0.9772.
The Addition Rule union
The Multiplication Rule intersection
Ordinary Least Squares (OLS)
Conditional Probability
Cov(X,Y) = σxy = E[(X – ux)(Y – uy)]
if σxy >0 then when X>ux, we also expect Y>uy
if σxy <0 then when X>ux, we also expect Y<uy and vice
versa
Residuals
Fitted value/ OLS regression line/ simple regression
function (SRF)
Residual sum of squares (SSR), represents variation not
explained by regression
Total sum of squares(SST), represents total variation
in the dependent variable
Coefficient of correlation= r =
Coefficient of determination= r2
Explained sum of squares(SSE), represents variation
explained by regression
measures the fraction of the total variation that is
explained by the regression
error var./ unconditional var./ disturbance var.
standard error of the regression(SER)
standard errors for regression coefficients