Exercise 1 (20 points). Consider the simple linear regression model without the intercept term: Y₁ =B₁x₁ + ₁, i=1,...,n where the variables e; are independent and identically distributed such that E[ei] = 0 and Var[ei] = 0². a) What is the additional constraint of this model compared to model (2.2) seen in class and what is its effect on the fitted line? b) Provide an example of a situation where the use of such a model seems appropriate. c) Write down the sum of squared residuals as well as the normal equation for this model and then find 3₁, the least squares estimator of 3₁. d) Calculate the expectation and the variance of 3₁. Is 3₁ a biased estimator?

Solved: Exercise 1 (20 points). Consider the simple linear regression model wi

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exercise 1 20 points consider the simple linear regression model witho

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Exercise 1 (20 points). Consider the simple linear regression model without the intercept term: Y₁ =B₁x₁ + ₁, i=1,...,n where the variables e; are independent and identically distributed such that E[ei] = 0 and Var[ei] = 0². a) What is the additional constraint of this model compared to model (2.2) seen in class and wh