A key assumption for the identification of the ceteris paribus effect in a multiple linear regression model, Yt = XtB + Et Homoskedasticity: Zero unconditional mean: Zero conditional mean: Simple random samplin: V (et) = 0² E(et |Xt) = 0 E(et | Xt) = 0 Cov(Et, Es) = 0

A key assumption for the identification of the ceteris paribus effect in a multiple linear regression model, Yt = XtB + Et Homoskedasticity: Zero unconditional mean: Zero conditional mean: Simple random samplin: V (et) = 0² E(et |Xt) = 0 E(et | Xt) = 0 Cov(Et, Es) = 0

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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General Cereals is using a regression model to estimate the demand for Tweetie Sweeties, a whistle-shaped, sugar-coated breakfast cereal for children. The following (multiplicative exponential) demand function is being used: QD= 6,280 P 1.35) 42.05 N 2.70 where QD quantity demanded, in 10-oz boxes P = price per box, in dollars A = advertising expenditures on daytime television, in dollars N = proportion of the population under 12 years old, in percent What is the point price elasticity of demand for Tweetie Sweeties? O 2.70 O 2.05 -0.66 -1.35 What is the advertising elasticity of demand? -1.35 O 2.70 O 0.76 O 2.05 According to the estimated model, a percent increase in the proportion of the population under 12 years old by percent. the quantity demanded
Given the estimated multiple regression equation ŷ = 6 + 5x1 + 4x2 + 7x3 + 8x4 what is the predicted value of Y in each case? a. x1 = 10, x2 = 23, x3 = 9, and x4 = 12 b. x1 = 23, x2 = 18, x3 = 10, and x4 = 11 c. x1 = 10, x2 = 23, x3 = 9, and x4 = 12 d. x1 = -10, x2 = 13, x3 = -8, and x4 = -16
You are given the following data: The regression equation is: A. -0.66 B. -1.20 (X'X)*¹ C. 1.12 O D. 2.06 = 1.3 2.1 0.8 -1.4 1.9 2.1 -1.4 s² = 0.86. T = 103 The correlation between ₁ and 3 (i.e., corr(Â₁, Â3)) is: -1.6] 1.9 (X'y) = 2.9 3.4 0.8 Yt = B₁ + B₂X2+ + B3X3t + Ut.
General Cereals is using a regression model to estimate the demand for Tweetie Sweeties, a whistle-shaped, sugar-coated breakfast cereal for children. The following (multiplicative exponential) demand function is being used: QD = 6,280 P(-2.15) A1.75N2.70 where QD = quantity demanded, in 10-oz boxes P = price per box, in dollars A = advertising expenditures on daytime television, in dollars N = proportion of the population under 12 years old, in percent What is the point price elasticity of demand for Tweetie Sweeties? 1.75 -1.23 2.70 -2.15 What is the advertising elasticity of demand? 0.65 1.75 -2.15 2.70 According to the estimated model, a percent increase in the proportion of the population under 12 years old by percent. the quantity demanded
A home appraisal company would like to develop a regression model that would predict the selling price of a house based on the age of the house in years (X1), the living area of the house in square feet (X2), and the number of bedrooms (X3). The following regression model was chosen using a data set of house statistics: y=88,399554791.3333x231,471.1372x3 The first house from the data set had the following values: Selling price $324,000 Age - 22 years Square Feet 2.000 Bedrooms 3 The residual for this house is 23,558 -41,480 10,216 -16,095 27
Consider a simple linear regression model, y = Bo + Bix+u.. What does the zero conditional mean assumption imply? The estimated average value of 31 is zero The expected value of the explained variable, y, is zero, regardless of what the value of the explanatory variable, x, is The expected value of the error term, u, is zero, regardless of what the value of the explanatory variable, x, is The estimated average value of 30 is zero
Finally consider the regression model with an extra covariate: Yi = Bo + B1x1i + B2x2; + €; Let 32=3.13, it's standard error s.e.(B1)=1.12 and assume n=811. Based only on this information, decide if it is useful to include X2i in the regression model. Carefully showing every step of your hypothesis test and explaining your answer. Use signifi- cance level a = .05.
When Y is regressed on X, B, > 0, sx+ 0, sy # 0, and the fraction of the variation in Y explained by the least-squares regression of Y on X does not equal 1. In this example, the sum of the squares of the deviations of the actual Y-values from their mean would definitely be greater than the sum of the squares of the deviations of the predicted Y-values from their mean. 1 A) B) true false 4. When Y is regressed on X, the sample slope is negative, sx + 0, sy + 0, and Y; = Y; for every observation. In this example, the sum of the squares of the deviations of the predicted Y-values from their mean would definitely be less than the sum of the squares of the deviations of the actual Y-values from their mean. A) В) true false 3.
46) The following model is a simplified version of the multiple regression model used by Biddle and Hamermesh (1990) to study the trade-off between time spent sleeping and working and to look at other factors affecting sleep: sleep = Bo + B₁totwrk + ß₂educ + ß3age +u, where sleep and totwrk (total work) are measured in minutes per week and educ and age are measured in years. (i) If adults trade off sleep for work, what is the sign of f₁? (ii) What signs do you think ₂ and 3 will have? (iii) Using the data in SLEEP75, the estimated equation is sleep = 6,241.15 + 0.211totwrk + 9.22educ + 1.67age n = 211, R² = 0.981 If someone works five more hours per week, by how many minutes is sleep predicted to fall? Is this a large tradeoff? (iv) Discuss the sign and magnitude of the estimated coefficient on educ. (v) Would you say totwrk, educ, and age explain much of the variation in sleep? What other factors might affect the time spent sleeping? Are these likely to be correlated with totwrk?
A. B. Consider data on births to women in the United States. Two variables of interest are the dependent variable, infant birth weight in ounces (bwght), and an explanatory variable, average number of cigarettes the mother smoked per day during pregnancy (cigs). The following simple regression was estimated using data on n = 1,388 births: bwght = 119.772 (0.572) n = 1,388, 0.514 cigs (0.091) R² = 0.0227, where standard errors are shown in parenthesis. What percent of the variation in birth weight is explained by cigs? What is the predicted birth weight when cigs = 0? What about when cigs = 20 (one pack per day)? Comment on the difference.
Consider the following regression model: wage-Bi+Bamalerpumalexedu Buedutu, where wage is the hourly wage measured in dollars: male is a dummy variable for males edu is the years of education: maleedu is the interaction of male and edu variables. The parameter estimates for B parameters are P-1.27: B1.29: Br-0,16: Be-0.82. What is the predicted marginal effect of years of education for males?
Consider the following sample regressions for the linear, the quadratic, and the cubic models along with their respective R2 and adjusted r2. Linear Quadratic Cubic Intercept 9.52 9.86 9.91 2.62 2.71 1.80 x2 NA -0.31 -0.33 x3 NA NA 0.26 R2 0.800 0.824 0.883 Adjusted R2 0.797 0.821 0.882 a. Predict y for x = 2 and 5 with each of the estimated models. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.) Linear ŷ Quadratic ŷ Cubic ý x = 2 x = 5