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Stochastic Error Term
a term that is added to a regression equation to introduce all of the variation in Y that cannot be explained by the included Xs.variation in Y not captured by X 1.Omitted variable 2.Measurement error 3.Incorrect functional form 4. Purely random and totally unpredictable occurrence TERM 2
Sampling distribution of hat
DEFINITION 2 Probability distribution of theses hat values across different samples. TERM 3
Type I
DEFINITION 3 Type I: We reject a true null hypothesis If =0 but you observe a hat that is very positive, you might reject a true null hypothesis, H0:0 is ture TERM 4
Type
II
DEFINITION 4 Type II: We do not reject a false null hypothesis if =1 but you observe a hat that is negative buy close to zero, you might fail to reject a false null hypothesis, H0: TERM 5
Partial regression coefficient
DEFINITION 5 Yi=0+1X1i+2X2i+3X3i+....+kXki+i Keeping 2 and 3 constant and changing 1 by one unit to see how much Yi changes. the 1 to k are the partial coefficeints
R^2bar or abjected R^
R^2bar=1-e2i/(N-K-1)/(Yi-Ybar)^2/(N-1) Measures the % of the variation of Y around its mean that is explained by the regression equation, adjusted for degrees of freedom. TERM 7
unbiased estimator
DEFINITION 7 An estimator hat its sampling distribution has as its expected value the true value of E(hat)= TERM 8
Review the literature and develop the
theoretical model
DEFINITION 8 Start with Theory then start your investigation where earlier researchers left off. Trace back from other papers that has to do with your topic TERM 9
Specify the Model: Select the independent
variables and the functional form
DEFINITION 9 independent variables and how they should be measured,the function form of the variables, and the properties of the stochastic error term TERM 10
Hypothesize the expected signs of the
coefficients
DEFINITION 10 Write out the regression model with hypothesized sign of the respective regression coefficient in a linear model like + or - above each coefficient
OLS squared
1.Sum of the residuals is exactly zero 2. OLS can be shown to be the best estimator possible under a set of specific assumptions. If meets all 7 assumption then OLS is BUE Square the residual (Y-Yhat)^ TERM 17
OLS Least
DEFINITION 17 Minimizing the squared residual TERM 18
Null & alternative
hypothesis
DEFINITION 18 Null hypothesis H0:0 (the values you expect 1+) (+) Reject H0 if Ftest>Fvalue Do not Reject H0 if Ftest< Fvalue TERM 19
T-test/T-statistic
DEFINITION 19 tk=(hatk-H0)/SE(hatk) (k=1,2...,K) tk=(hatk)/SE(hatk) (k=1,2...,K) SE(hatk)= est. standard error of hatk H0=border value(usually zero) implied by the null hypothesis hatk=est. regression coefficient of the kth variable TERM 20
F-test
DEFINITION 20 ((RSSm-RSSu)/m)/(RSSu/(N-K-1)) H0:B1=B2=B3= HA:otherwise (ESS/k)/(RSS/(N-K-1))=Ftest R^2=ESS/TSS... TSS=ESS+RSS... ESS=RSS(R^2)/(1-R^2) get Fvalue. compare Ftest to Fvalue reject null if Ftest >Fvalue
T-test
Yhati=1coefficient+2coefficientXi H0:1=0 HA: Tstat=1/SE(1) Tcrit=from book, from alpha and DF TERM 22
Ramsey's test
DEFINITION 22 Make the model, find yhat,find yhat^2,3,4,, est. The model with them. ((RSSm-RSSu)/m)/(RSSu/(N-K-1))= fstat RSSm from the nonYhat RSSu from the Yhat m the # of restriction applied TERM 23
model is mis-specified from Ramsey's test
DEFINITION 23 if the Ftest >the fvalue here on the ramsey test then you can reject the null hypothesis that the coefficients of the added variables are jointly zero leaving out something important such as beef prices. TERM 24
result if you omit a variable? Consequences?
DEFINITION 24 causes bias in the estimated coefficients of the variables that are in the equation. force the expected value of the estimated coefficient away from the true value of the population coefficient. IF you leave out a variable then it will go into the error term and when that omitted variable changes then the error term and the other non omitted variables will change. violating Classical assumption TERM 25
Aic and sc
DEFINITION 25 Aic=ln(RSS/N)+2(K+1)/N Sc=ln(RSS/N)+ln(N)(K+1)/N
