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# Intro to Interntl Relations PLS 160

MSU

GPA 3.93

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This 5 page Class Notes was uploaded by Fabian Hills on Saturday September 19, 2015. The Class Notes belongs to PLS 160 at Michigan State University taught by Staff in Fall. Since its upload, it has received 53 views. For similar materials see /class/207463/pls-160-michigan-state-university in Political Science at Michigan State University.

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Date Created: 09/19/15

Regression Analysis Spring 2000 By Wonjae 0 Purposes a Explaining the relationship between Y and X variables with a model Explain a variable Y in terms of Xs b Estimating and testing the intensity of their relationship c Given a xed x value we can predict y value How does a change of in X affect Y ceteris paribus By constructing SRF we can estimate PRF 0 OLS ordinary least squares method A method to choose the SRF in such a way that the sum of the residuals is as small as possible Cf Think of trigonometrical function and the use of differentiation 0 Steps of regression analysis 1 Determine independent and dependent variables Stare one dimension function model 2 Look that the assumptions for dependent variables are satis ed Residuals analysis a Linearity assumption 1 b Normality assumption 37 draw histogram for residuals dependent variable or normal PP plot Spss9statistics9regression91inear9plots9 Histogram Normal PP plot of regression standardized c Equal variance homoscedasticity assumption 47draw scatter plot for residuals Spss statistics9regression91inear9plots Y ZRESID X ZPRED Its form should be rectangular If there were no symmetry form in the scatter plot we should suspect the linearity d T 1r 1 Jquot 56 no 39 quot between the disturbances zero covariance between error term and Xieach individual should be independent 5 Look at the correlation between two variables by drawing scatter graph Spss graph scatter simple a Is there any correlation b Is there a linear relation c Are there outliers 9 If yes clarify the reason and modify it We should make outliers dummy as a new variable and do regression analysis again d Are there separated groups 9 If yes it means those data came from different populations 4 Obtain a proper model by using statistical packages SPSS 5 Test the model a Test the significance of the model the signi cance of slope F Test In the ANOVA table nd the f value and p valuesig If pvalue is smaller than alpha the model is significant b Test the goodness of fit of the model In the Model Summary look at R square R squarecoef cient of determinationilt measures the proportion or percenng of the total variation in Y explained by the regression model If the model is signi cant but R square is small it means that observed values are widely spread around the regression line 6 Test that the slope is signi cantly different from zero a Look at tvalue in the Coefficients table and nd pvlaue b Tsquare should be equal to Fvalue 7 If there is the signi cance of the model Show the model and interpret it 0 steps a Show the SRF b In Model Summary 9 Interpret R square c In AN OVA table9 Show the table interpret Fvalue and the null hypothesis d In Coefficients table9 Show the table and interpret beta values e Show the residuals statistics and residuals scatter plot If there is no signi cance of the model interpret it like this Xvariable is little helpful for explaining Y variable or There is no linear relationship betweenX variable anal Y variable 8 Mean estimation prediction and individual prediction We can predict the mean individuals and their con dence intervals Spss 9statistics 9regression9 linear save predicted values unstandardized Testing a model Wonjae 0 Before setting up a model 1 Identify the linear relationship between each independent variable and dependent variable 9 Create scatter plot for each X and Y STATA plot Y X1 plot Y X2 ovtest rhs graph Y X1 X2 X3 matrix avplots 2 Check partial correlation for each X and Y STATA pcorr Y X1 X2 pcorr X1 Y X2 pcorr XzY X1 0 A er setting up a model 1 Testing whether two different variables have same coef cients 9 The null hypothesis is that X1 and X2 variables have the same impact on Y STATA test X1 X2 2 Testing Multicollinearity Gujarati p345 1 Detection I High R2 but few signi cant tratios I High pairwise zeroorder correlations among regressors STATA regress Y X1 X2 X3 graph Y X1 X2 X3 matrix avplots I Examination of partial correlations I Auxiliary regressions I Eigenvalues and condition index I Tolerance and variance in ation factor STATA regress Y X1 X2 X3 vif Interpretation If a VIF is in excess of 20 or a tolerance 1VIF is 05 or less There might be a problem of multicollinearity 2 Correction A Do nothing I If the main purpose of modeling is predicting Y only then don t worry since ESS is left the same I Don t worry about multicollinearity if the R squared from the regression exceeds the R squared of any independent variable regressed on the other independent variables I Don t worry about it if the tstatistics are all greater than 2 Kennedy Peter 1998 A Guide to Econometrics 187 01 Incorporate additional information I After examining correlations between all variables nd the most strongly related variable with the others And simply omit it STATA corr X1 X2 X3 9 Be careful of the specification error unless the true coefficient of that variable is zero I Increase the number of data I Formal ize relationships among regressors for example create interaction terms 9 If it is believed that the multicollinearity arises from an actual approximate linear relationship among some of the regressors this relationship could be formalized and the estimation could then proceed in the context of a simultaneous equation estimation problem Speci a relationship among some parameters If it is wellknown that there exists a speci c relationship among some of the parameters in the estimating equation incorporate this information The variances of the estimates will reduce Form a principal component Form a composite index variable capable of representing this group of variables by itself only if the variables included in the composite have some useful combined economic interpretation Incorporate estimates from other studies See Kennedy 1998 188189 Shrink the OLS estimates See Kennedy 3 Heteroscedasticity 1 Detection I Create scatter plot for residual squares and Y p368 I Create scatter plot for each X and Y residuals standardized Partial Regression Plot in SPSS STATA predict rstan plot X1 rstan plot X2 rstan I White s test p379 Step 1 regress your model STATA reg Y X1 X2 Step 2 obtain the residuals and the squared residuals STATA predict resi gen resi2 resi 2 Step 3 generate the tted values yhat and the squared tted values yhat STATA predict yhat gen yhat2 yhat 2 Step 4 run the auxiliary regression and get the R2 STATA reg resi2 yhat yhat2 Step 5 1 By using f statistic and its pvalue evaluate the null hypothesis or 2 By comparing xzcalmmed n times R2 with xzmmal evaluate it again If the calculated value is greater than the critical value reject the null there might be heteroscedasticity or speci cation bias or both I Cook amp Weisberg test STATA regress Y X1 X2 X3 hettest I The Breusch Pagan test STATA reg Y X1 X2 predict resi gen resi2 resi 2 reg res2 X1 X2 2 Remedial measures I when variance is known use WLS method STATA reg Yquot X0 X1 noconstant cf Y YB X XB I when variance is not known use white method STATA gen X2r sqrtX gen dX2r 1X2r gen Yquot YX2r reg Yquot dX2r X2r noconstant 4 Autocorrelation 1 Detection I Create plot STATA predict resi resi gen lagged resi resiLn l plot resi lagged resi I DurbinWatson d test Run the OLS regression and obtain the residuals 9 compute d 9 nd dun cal and dUValues given the N and K 9 decide according to the decision rules

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