|Consider the following simple regression model y= Bo + B1x1 + u and z is an instrument for x. Suppose x and z are both positively correlated with u and Corr(z,x) > 0. Then, the asymptotic bias in the IVestimator is less than that for OLS only if:a. Corr(z,u)/ Corr(z,x) = Corr(x,u).O b. Corr(z,u)/ Corr(z,x) < Corr(x,u).O c. Corr(z,u)/ Corr(z,x) # Corr(x,u).O d. Corr(z,u)/ Corr(z,x)> Corr(x,u).

Given Information: Consider the simple regression model: y=β0+β1x1+u (z is an instrument…

Answered: Consider the following simple…

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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A recent Gallup survey of a random sample of Americans (18 and older) found that the average number of alcoholic drinks consumed per week (drinks) by males was 4.2 and by females was 1.4.[¹] Suppose we use the underlying survey data to estimate a least-squares regression of the average number of drinks a person reports consuming per week (Drinks;) on a dummy variable equal to 1 if i is female and 0 otherwise (Female;). (Assume all respondents identify as either male or female.) The estimated regression line equation can be written as: Drinks = a +bFemale Alcohol Consumption by Gender What is the numerical value of b?
Suppose that you run a regression of Y, on X, with 110 observations and obtain an estimate for the slope. Your estimate for the standard error of ₁ is 1. You are considering two different hypothesis tests: The first is a one-sided test: Ho: B1-0, Ha: 31>0, a = .05 The second is a two-sided test: Ho: 31-0, Ha: B1 0,a = .05 (a) What values of , would lead you to reject the null hypothesis in the one-sided test? (b) What values of , would lead you to reject the null hypothesis in the one-sided test? (c) What values of would lead you to reject the mill hypothesis in the one-sided test, but not the two-sided test? (d) What values of 3 would lead you to reject the null hypothesis in the two-sided test, but not the one-sided test?
For x={1 2 3 4 5} and y={2 1 4 3 6} use normal equation (c =(ATA)-1ATy) to find with: a-) linear regression coefficients, b-) the linear regression equation, c-) residel sum of squares(RSS)
Suppose x1 ans x2 are predictor variables for a response variable y. a. The distribution of all possible values of the response variable corresponding to particular values of the two predictor variables is called a distribution of the response variable. b. State the four assumptions for multiple linear regression inferences.
1. Consider two least-squares regressions and y = Xíễ tế y = Xí$i+ XzB2 tê Let R2 and R2 be the R-squared from the two regressions. Show that R22 R2.
The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.7 8.1 6.7 3.3 2.7 2.3 2.2 0.3 yy 13.8 10.7 9.9 6.6 6.1 5.9 6.1 4.5 xx = thousands of automatic weaponsyy = murders per 100,000 residents Determine the regression equation in y = ax + b form and write it below. (Round to 2 decimal places) A) How many murders per 100,000 residents can be expected in a state with 6.4 thousand automatic weapons? Answer = Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 6.7 thousand automatic weapons? Answer = Round to 3 decimal places.
A company studying the productivity of its employees on a new information system was interested in determingg if the age (X) of data entry opeertors influenced the number of completed entries made per hour (Y). The regression equation is y = 14.374 - 0.145x Suppose the acyual completed entries per hour for an operator who is 35 years old was 8. The residual is:
Suppose that n = 100 i.i.d. observations for (Y, X) yield the following regression results: Ŷ 32.1 + 66.8X, SER = 15.1, R² = 0.81. = (15.1) (12.2) Another researcher is interested in the same regression, but he makes an error when he enters the data into his regression program: He enters each observation twice, so he has 200 observations (with observation 1 entered twice, observation 2 entered twice, and so forth). a. Using these 200 observations, what results will be produced by his regression program? (Hint: Write the "incorrect" values of the sam- ple means, variances, and covariances of Y and X as functions of the "correct" values. Use these to determine the regression statistics.) Ŷ - X, SER = 6tc () () b. Which (if any) of the internal validity conditions are violated?
Suppose we carry out a linear regression analysis with the following model: Y = Bo + B1X1 + .. + BrXr + € where k = 8. n = 195. We find SSReg = 231.4, and SSTotal = 972.5. Before collecting the data, we knew that we'd like to test the null hypothesis that Bi = B2 = 63 = 0. If we run a regression model leaving the predictors associated with these slopes out of the model, we find SSReg = 74.1 and SSTotal = 972.5. What is the value of the appropriate Fstatistic to test this null hypothesis (that these 3 slopes are 0)?
A group of scientists wants to determine the efficacy of a vaccine. To do they recruited 1000 subjects. Two months ago 300 random subjects received the vaccine T = 1. The other 700 received a placebo T = 0. The scientist also measured if the subjects became infected with the virus Y = 1 or not Y = 0 in the last 2 months. They plan to test the efficacy of the vaccine by running the following regression: Y = Bo + Bit tu Which of the following statements is FALSE: Select one: a. This model will generate biased estimates because it does not control for many omitted variables Ob. The fact that more people receive the placebo than the vaccine will not generate bias Scientists do not need to observe the initial health status of the subjects to get unbiased estimates because the assignment of the vaccine was random O d. A negative B₁ would indicate that the vaccine is effective c.

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