A dependent variable is regressed on K independent variables, using n sets of sample observations. We denote SSE as the error sum of squares and R2 as the coefficient of determination for this estimated regression. We want to test the null hypothesis that K1 of these independent variables, taken together, do not linearly affect the dependent variable, given that the other (K – K1) independent variables are also to be used. Suppose that the regression is reestimated with the K1 independent variables of interest excluded. Let SSE* denote the error sum of squares and R*2, the coefficient of determination for this regression. Show that the statistic for testing our null hypothesis, introduced in Section 12.5, can be expressed as follows:
Answer to relevant QuestionsThe following model was fitted to a sample of 30 families in order to explain household milk consumption: y = β0 + β1x1 + β2x2 + ε where y = milk consumption, in quarts per week x1 = weekly income, in hundreds of ...Consider the following two equations estimated using the procedures developed in this section: i. yi = 4x1.5 ii. yi = 1 + 2xi + 2x2i Compute values of yi when xi = 1, 2, 4, 6, 8, 10. The following model was estimated for a sample of 322 supermarkets in large metropolitan areas (Macdonald and Nelson 1991): where y = store size x = median income in zip-code area in which store is located The number in ...What are the model constant and the slope coefficient of x1 when the dummy variable equals 1 in the following equations, where x1 is a continuous variable and x2 is a dummy variable with a value of 0 or 1? a. y` = 4 + 9x1 + ...In a survey of 27 undergraduates at the University of Illinois the accompanying results were obtained with grade point averages (y), the number of hours per week spent studying (x1), the average number of hours spent ...
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