GIve Proof of the Gauss–Markov Theorem for Multiple Regression?
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GIve Proof of the Gauss–Markov Theorem for Multiple Regression?
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- Consider the linear model y=B,+B,x,+B,x,+B,x+P+u, You estimate the model y=B,+B,x,+B,x, observations and obtain the OLS residuals . You then estimate the auxiliary regression +u based on 123 31 3 31 44i The LM statistic 3i +1 4/ you obtain to test the null hypothesis that H:B,=B,=0 is 20.91. What is the R2 of the auxiliary regression? It is not possible to say 0.17 O 0.175714 O 0.177203The following are all benefits of generalized additive models (GAMs), EXCEPT: Group of answer choices a)GAMs are less computationally demanding than linear regression. b)GAMs can model non-linear relationships that standard linear regression will miss. c)GAMs can potentially make more accurate predictions of the response than linear regression can. d)One can examine the effect of each predictor on the response individually while holding all of the other predictors fixed.Can you help me solve sub-part C
- In the simple linear regression model , the Gauss Markov ( classical ) assumptions guarantee that the OLS estimator of the unknown parameters is BLUE. Among those assumptions , in order to have consistency of the OLS estimator we need ( this is a question on the necessary condition ): Question 4Select one: a. we need that the errors are not correlated with each others and that they have zero mean b. we need that the errors are homoscedastic ( all have the same variance) c. we need that the residuals are not correlated with the explanatory variables and that the residuals have zero mean d. we need that the errors have zero mean and that they are not correlated with the regressors ( no endogeneity) e. we need that the errors are homoscedastic ( all have the same variance) and not correlated with each others ( no serial correlation)5After 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.
- uppose there is a random sample of n observations, divided into four groups. The table below summarizes the count of observations that were seen in each group. Group 1 Group 2 Group 3 Group 4 27 27 59 31 We are interested in testing the null hypothesis H0:p1=p2=p3=p4=0.25H0:p1=p2=p3=p4=0.25, against the alternative hypothesis HA:AtleastoneproportionisincorrectHA:Atleastoneproportionisincorrect. What is the expected count for each of the groups? Expected: What is the value of the test statistic? Round your response to at least 2 decimal places. What are the appropriate degrees of freedom? What is the P-value? Round to at least 4 decimal placesWhat is the coefficient of determination of the least squares regression model for the data in the scatterplot? 0.8554 0.9273 0.9143 0.9463Consider 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
- 1. Derive the least squares estimators (LSES) of the parameters in the simple linear regression model. 2. Derive the estimators of 30 and ß1 using maximum likelihood estimation procedures.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 doesnt 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 didnt use a high enough con dence level