You can add the fitted regression line manually into

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You can add the fitted regression line manually into the Warwick scatter. Right-click anywhere in the plot, and select Edit . On the default Main tab, you should see an option fitted line with the current entry of none —as no relationship exists between x and y here. Click on the download arrow and select linear: y = a + b*x , and click on OK . 9. Estimate the same regression model as you did for the Leicester sample, and conduct the same hypothesis test. What conclusion do you draw from the test and estimation outcome? 10. The Leicester and Warwick samples should have given you similar estimates for β . Despite this, you should have obtained very different conclusions regarding the influence advertising expenditure has on sales revenue from the two samples. What are the reasons for this? Which sample gives a more reliable estimate of the parameters and why? Consider which dataset gives a more accurate estimation of the parameters, particularly ˆ β . Recall that the accuracy or reliability of an estimator is given by its variance. We have just seen above that the variance of ˆ β is estimated by ˆ σ 2 β = n 1 ˆ 2 i ( n - 2) n 1 ( x i - x ) 2 It is inversely related to n and the sample variance of x , and positively related to the sum of squares of residuals. Open the pdf file of the xy scatter of the Leicester sample you saved earlier in Adobe Reader (as you can’t run two different sessions of gretl on one machine at the same time) and compare the two pictures. What really is contributing to the large standard error of ˆ β for the Warwick sample? 6
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