Hi can you please help me with these questions?

Assignment 6 Deadline 23. I will collect the hardcopy from students who attend on Sept 23 morning class. 1. Suppose the true regression model is y = 50 + lxl + ax; + It. In addition, the Gauss- Markov assumptions are satised. A researcher accidentally excluded as; variable from the regression model and used a \"wrong" regression model y = [30 + 31x1 + v. (a) Let the 31 be the OLS estimators from the regression y on x1 only. Derive the estimator 31. (b) State the minimal assumptions that make [3'1 unbiased. You need to justify your answer. (c) Suppose x1 and x2 are positively correlated, and 52 has a positive theoretical sign. Show that 31 is biased and on average it overestimates the true [3'1 population parameter. [Difculty Level: 3.5] 2. The general formula for the sampling variance of the OLS estimator is Va'rogj) = m. _ J' (a) Show that when the model is a simple regression model, the sampling variance of the OLS 0'2 estimator degenerates to Varml) = m. (b) Consider a regression model with 2 explanatory variables. What is the consequence of having two highly correlated explanatory variables? How would you solve the \"problem"? (c) Explain Variance Ination factor (VIF). What is the signicance of VIP? [Hint: study Chapter 3-] [Difculty Level: 3.0] 3. A brochure inviting subscriptions for a new diet program states that the participants are expected to lose over 10.00 kg in three months. From the data of the three-month weight control program, we interviewed 200 participants about their weight loss. The sample mean and sample standard deviation are found to be 8.80 kg and 25.00 kg, respectively. Could the statement in the brochure be substantiated on the basis of these ndings? Please test Ho: ,u = 10 against H1: 1.;