Question

1. What is the coefficient of determination and why is it important? What does it show us? 2. What is heteroskedasticity, which assumption of the linear model does it violate, and how can we test for it? 3. What is multicollinearity? What problems can it cause to our results? 4. If you decide to scale both your dependent and your independent variable by 100, how will your regression results change? 5. Using N=40 observations, you estimate the following model y = B1 + B2x + B3z + e and obtain SSE = 979.83 andsy = 13.45222, where sy = {(yi - y)2/(N − 1). Find a. R b. Conduct an F-test for testing Ho: B2 = 0,33 = 0 and state your conclusion. c. Consider again the above model. After augmenting this model with the squares and cubes of predictions yềand ŷ3, we obtain SSE = 696.5357. Use RESET to test for misspecification. 6. Consdier the following model y = B1 + B2X2 + B3X3 + e and suppose that application of least squares to 20 observations on these variables yields the following results ( cov(b) denotes the estimated covariance matrix):

Answer 1

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Answer 1 - We measure the goodness of fit of the estimated regression equation by using the r2 statistic, where r is the value of simple correlation coefficient between Yi and Xi. R2 is the ratio of ESS to TSS, which shows the proportion of total variation in dependent variable which is explained by the independent variable of the model. r2 is known as coefficient of determination and is given by: r2 = ESS/TSS = 1 - (el)/ (y2) The coefficient of determination always lies between 0 and 1. When the value of r2 is 0, no part in the dependent variable is explained by the variation in the independent variable of the model. On the other hand, when the value of r2 is 1, the entire part of variation in the dependent variable is explained by the variation in the independent variable of the model. It is very important because it helps us determine whether the estimated regression line is a good fit. When the value ofr2 is close 1, we can conclude that we have a good fit estimated line and if it is close to 0, we can conclude that the estimated line does not provide a good fit.