GIve Proof of the Gauss–Markov Theorem for Multiple Regression?

After ingesting 15 mL of 95% alcohol, the blood alcohol level of a 75 kg adult male rises rapidly to a maximum level then gradually decreases over time. Measurements of the subject's blood alcohol level at time t (in minutes) since the maximum blood alcohol level was observed gave the following results: Time t (in minutes) Blood alcohol level, B (in mg/L) 10 25 60 70 90 150 160 130 70 60 40 20 a) Using least squares regression, determine an equation of the form B= Be-kt that best fits the relationship shown. You do not need to graph the data. (Note any transformations you have applied to your data: x→, y→, round the values that appear in your final equation to three significant figures, and use the correct variable names...not x and y.)| b) Using your equation from part a), estimate the time t at which the subject's blood alcohol level will be 90 mg/L? Round your answer to the nearest minute.

What is the coefficient of determination of the least squares regression model for the data in the scatterplot? 0.8554 0.9273 0.9143 0.9463

Consider the multiple regression model Y a + B1 X1 + ß2 X2 + u . When omitting X2 from the regression, then there will be omitted variable bias for B Only if X1 and X2 are correlated, and ß1 # 0 Only if X1 and X2 are correlated, and B2 + 0 Only if X1 and X2 are correlated, ß1 # 0 and B2 # 0 O Only if ß1 + 0 and ß2 # 0

Prove that b is an unbiased estimator for ß. What are the essential conditions to prove ordinary least squares (OLS) estimator is unbiased? E(b) = ß

Phoebe gathers data and estimates many di¤erent regression models. All of them suggest that children who have more books at home have fewer cavities. Phoebe doesn’t think this result is important because: a.) There is clearly selection bias, kids who have lots of books at come from higher income and better educated families.b.) The data on cavities is certainly heteroskedasticc.) Phoebe only used ordinary least squares in her model, should have used weighted least squares d.) Phoebe didn’t use a high enough con…dence level

What are the difficulties in estimating the following model? Use as much detail as possible in answering this question while considering the Gauss-Markov assumptions and OLS estimator.   Economic productivity = β0 + β1Unemployment + β2Innovation + θiControls + ei   Where unemployment is the average unemployment rate of a country and innovation is an index of R&D performance.