5. In class, we showed that was consistent. There's more than one way to do this!...

 

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5. In class, we showed that was consistent. There's more than one way to do this! (a) (5 points) Show, using the law of large numbers, that the sample covariance is consistent for the population covariance. (Hint: expand them; strategy 1) (b) (5 points) Do the same thing to show that the sample standard deviation Sx is consistent for the population sample deviation, ox (c) (5 points) Combine the results above to provide an alternative proof that is consistent in a simple regression. 6. (10 points) Show that Bo is consistent for Bo. Total for Question 5: 15 7. In Case Study 1, Reka reports standardized coefficients in Table 1, which are in italics in the case study. A standardized coefficient, Bk is defined as: Bk=Bk Yi (a) (5 points) What is the interpretation of Bk in a model; i.e. for a 1-unit change in Bk, what is the change in Y? You may want to express this in other units, or by transforming the model. (Hint: chain rule) (b) (5 points) Show that the sample analogue estimate of B is consistent. (c) (5 points) Why would you want to do this? Explain. Activate 5. In class, we showed that was consistent. There's more than one way to do this! (a) (5 points) Show, using the law of large numbers, that the sample covariance is consistent for the population covariance. (Hint: expand them; strategy 1) (b) (5 points) Do the same thing to show that the sample standard deviation Sx is consistent for the population sample deviation, ox (c) (5 points) Combine the results above to provide an alternative proof that is consistent in a simple regression. 6. (10 points) Show that Bo is consistent for Bo. Total for Question 5: 15 7. In Case Study 1, Reka reports standardized coefficients in Table 1, which are in italics in the case study. A standardized coefficient, Bk is defined as: Bk=Bk Yi (a) (5 points) What is the interpretation of Bk in a model; i.e. for a 1-unit change in Bk, what is the change in Y? You may want to express this in other units, or by transforming the model. (Hint: chain rule) (b) (5 points) Show that the sample analogue estimate of B is consistent. (c) (5 points) Why would you want to do this? Explain. Activate