(c) True of False. If Var(U) = o and Var(U|X.) = X²o?, and we usethe homoskedastic-only formula to compute the standard errors, thenthe OLS estimator B1 will be unbiased but inconsistent.(d) Suppose that you know Bo B1. Derive a formula for the least squaresestimator of B1.!! Question 3. Basics about OLS.You have a dataset of i.i.d. observations (Y,, X;), whereY; = Bo + B1 X; + U4.Suppose that the three key assumptions of OLS hold. In particular, E(U;|X;) =0.(a) Prove that E(U) = 0.(b) Prove that E(X?U.) = 0.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider a two-dimensional scatterplot representing the relationship between two continuous variables. If the correlation coefficient is -1, then: a. All points lie in a straight line with a slope of -1. b. All points lie in a straight line with an unknown negative slope. c. All points do not lie in a straight line but the best fitting regression line has a slope of -1 d. There is a strong positive relationship between the two variables.
The marketing research department of a large company knows that the company's monthly sales are influenced by the way in which it spends money on marketing. For example, monthly expenditures such as the ones listed below are known to have an effect on y, the company's total monthly sales (in millions of dollars). x = money spent on television advertising (in 1000's of dollars) X2 = money spent on promotion (i.e., free samples) x3 = money spent on newspaper advertising (in 1000's of dollars) X = average discounts offered to retail outlets (in %) Using data from the previous 26 months, the company decides to collect data on 3 of the independent variables to use in a multiple regression model for estimating monthly sales. If the R´ for this model is 0.5, fill in the missing entries in the ANOVA table associated with this model. Do all calculations to at least three decimal places. Source of variation Degrees of freedom Sums of Mean F statistic squares squares Regression Error Total 4+
Question 2 Find the line of best fit for the data set: (1,2), (2,3), (4,1). y = 3 – x Oy = 2 - Oy = 3 –z Oy =2-z
If x and y are two correlated variables with S.D. 0, and o, and Ox Oy correlation coefficient p, find the correlation between ax + by · and are 9. cx + dy, a, b, c, d being constants. Find k for which x+ ky and x +y uncorrelated.
he table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.3 8.5 7.2 3.4 2.5 2.7 2.1 0.5 yy 13.7 11 10.2 7.2 5.9 6.5 5.6 4.7 xx = thousands of automatic weaponsyy = murders per 100,000 residentsThis data can be modeled by the equation y=0.84x+4.09.y=0.84x+4.09. Use this equation to answer the following;A) How many murders per 100,000 residents can be expected in a state with 9 thousand automatic weapons?Answer = Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 2.9 thousand automatic weapons?Answer = Round to 3 decimal places. Submit QuestionQuestion 18

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You have a dataset of i.i.d. observations (Y, X), where Y; = Bo + B1 X; + U4. %3D Suppose that the three key assumptions of OLS hold. In particular, E(U,|X;) = 0. %3D