A dependent variable is regressed on two independent variables. It is possible that the hypotheses H0: β1 = 0 and H0: β2 = 0 cannot be rejected at low significance levels, yet the hypothesis H0: β1 = β2 = 0 can be rejected at a very low significance level. In what circumstances might this result arise?
Answer to relevant QuestionsSuppose that the regression model y = β0 + β1x1 + β2x2 + ε is estimated by least squares. Show that the residuals, ei, from the fitted model sum to 0. At the end of classes professors are rated by their students on a scale of 1 (poor) to 5 (excellent). Students are also asked what course grades they expect, and these are coded as A = 4, B = 3, and so on. The data file ...The Economics Department wishes to develop a multiple regression model to predict student GPA for economics courses. Department faculty have collected data for 112 graduates, which include the variables economics GPA, SAT ...The data file Income Canada shows quarterly observations on income (Y) and money supply (X) in Canada. Estimate the model (Hsiao 1979) yt = β0 + β1xt + γyt-1 + εt and write a report on your findings. Based on data from 63 counties, the following model was estimated by least squares: where y` = growth rate in real gross domestic product x1 = real income per capita x2 = average tax rate, as a proportion of gross national ...
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