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# Hypothesis Testing

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Regression Analysis Tutorial LECTURE DISCUSSION Hypothesis Testing Econometrics Laboratory C University of California at Berkeley C 22 26 March 1999 109 Regression Analysis Tutorial 110 Introduction Consider the model you estimated in the previous workshop The output for the first model is Dependent variable USAGE Current sample 1 to 500 Number of observations 500 Mean of dependent variable Std dev of dependent var Sum of squared residuals Variance of residuals Std error of regression R squared Adjusted R squared Durbin Watson statistic F statistic zero slopes Schwarz Bayes Info Crit Log of likelihood function Variable C AC CDD NEMPLOY SQFT Estimated Coefficient 127568 20606 7 23 9860 6 61867 931 616 229970 91538 8 362272E 13 731863E 10 85549 0 133589 126588 2 06459 19 0806 22 7658 6385 38 Standard Error 15133 6 8116 66 4 80534 89 4999 147 957 t statistic 8 42949 2 53882 4 99152 073952 6 29652 The point estimates are in the first column of numbers This lecture introduces you to the use of the other columns Econometrics Laboratory C University of California at Berkeley C 22 26 March 1999 Regression Analysis Tutorial 111 The second column gives numbers that describe the statistical precision of the point estimates Because the regression relationship includes a disturbance term one cannot estimate the coefficients on the explanatory variables exactly If a new data set were collected and the same regression coefficients re estimated the new estimates would not equal the initial ones because the OLS estimators are random variables The second column contains estimates of the standard deviations of each OLS regression coefficient these estimates are commonly called standard errors A common rule of thumb is that the actual regression coefficient is probably within two standard errors of its point estimate Thus the actual audit impact is probably between 4 375 and 36 839 Econometrics Laboratory C University of California at Berkeley C 22 26 March 1999 Regression Analysis

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