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45-733 PROBABILITY AND STATISTICS I

============================================================ Dependent Variable: GNP Method: Least Squares Date: 02/25/99 Time: 15:49 Sample: 1915 1988 Included observations: 74 ============================================================ Variable CoefficientStd. Errort-Statistic Prob. ============================================================ C 3.025348 0.547696 5.523772 0.0000 (1) MILMOB 3.697863 0.547363 6.755782 0.0000 ============================================================ R-squared (2) 0.387966 Mean dependent var 3.061841 (3) Adjusted R-squared 0.379466 S.D. dependent var 5.980692 (4) S.E. of regression 4.711230 Akaike info criter 5.964430 Sum squared resid 1598.089 Schwarz criterion 6.026702 Log likelihood (5) -218.6839 F-statistic 45.64060 (6) Durbin-Watson stat 1.266900 Prob(F-statistic) 0.000000 (7) ============================================================

- This is the two-tail P-Value for the null hypothesis in the
hypothesis test:

has at t-distribution with n-k-1 degrees of freedom (k = number of**H**_{0}: b_{0}= 0 H_{1}: b_{0}¹ 0 where_{Ù}_{Ù}(b_{0}- b_{0})/(VAR(b_{0})^{1/2}*independent*variables excluding the constant). The test statistic here is just the coefficient value divided by the standard error:

Test Statistic = 3.025348/.547696 = 5.523772

If you issued the EViews command:

Scalar PVal=@TDIST(5.523772,72)

you would get the two-tail P-Value = .000000499.

Hence, in EViews -- as is the case with almost all stat packages -- the column labeled "Prob" is simply the two-tail P-Values for the null hypothesis that the corresponding coefficient is equal to zero. It is then up to you to interpret this substantively!

- R-squared. This is literally the squared correlation
coefficient:
_{ Ù }_{Ù}r^{2}= COV(Y,Y)^{2}/[VAR(Y)VAR(Y)], where_{Ù}Y = GNP and Y is the estimated GNP based on the above equation:_{Ù}GNP = 3.025348 + 3.697863*MILMOB - Mean dependent var. This is literally the sample mean
discussed in class:
**_****Y**= S_{n}_{i=1,n}Y_{i}/n Note that the sample size, n, here is equal to 74. - S.D. dependent var: This is the unbiased estimator formula
discussed in class:
_{_}s_{y}= {[å_{i=1,n}(y_{i}- Y_{n})^{2}]/(n -1)}^{1/2} - Log likelihood. This is the value of the log of the likelihood
function:

**L(e**where in this example_{1}, e_{2}, ... , e_{n}| b_{0}, b_{1}) = ln{f(e_{1}, e_{2}, ... , e_{n}| b_{0}, b_{1})}

**e**Here_{i}= y_{i}- b_{0}- b_{1}x_{i}and e_{i}~ N(0, s^{2})**y = GNP**and**x = MILMOB**. The idea is to find estimates of the coefficients -- the**b**s -- that maximize the likelihood function.

- F-statistic. This is the overall F-Statistic of the regression.
It is the ratio:

**[r**Where^{2}/k]/[(1 - r^{2})/(n - k - 1)]**r**is the R-squared of the regression explained in point (1) above; k = number of independent variables (excluding the constant or intercept term); and n = sample size.^{2}

- This is the upper-tail P-Value for the F-Statistic.