Consider a simple linear regression model that can be written as Yi=Bi+Bxit&, i=1.2,...,n, where B and...

 

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Consider a simple linear regression model that can be written as Yi=Bi+Bxit&, i=1.2,...,n, where B and are unknown parameters, &; ~N(0, ) are the random error terms, i denotes the number of observations, and n is the sample size. (i) If you multiply all the x values by 20, but not the y values, show mathematically what happens to the parameter values of B and and explain your results. What will happen to the least squares estimates of b and b? What happens to the variance of the error term? (ii) If you multiply all the y values by 20, but not the x values, show mathematically what happens to the parameter values of B and and explain your results. What will happen to the least squares estimates of b and b? What happens to the variance of the error term? [4] [4] Consider a simple linear regression model that can be written as Yi=Bi+Bxit&, i=1.2,...,n, where B and are unknown parameters, &; ~N(0, ) are the random error terms, i denotes the number of observations, and n is the sample size. (i) If you multiply all the x values by 20, but not the y values, show mathematically what happens to the parameter values of B and and explain your results. What will happen to the least squares estimates of b and b? What happens to the variance of the error term? (ii) If you multiply all the y values by 20, but not the x values, show mathematically what happens to the parameter values of B and and explain your results. What will happen to the least squares estimates of b and b? What happens to the variance of the error term? [4] [4]