2 In the simple linear regression model y = Bo + Bjx + u, suppose that E(u) + 0. Letting a, = E(u),show that the model can always be rewritten with the same slope, but a new intercept and error, wherethe new error has a zero expected value.3 The following table contains the ACT scores and the GPA (grade point average) for eight college stu-dents. Grade point average is based on a four-point scale and has been rounded to one digit after thedecimal.StudentGPAACT12.82123.42433.02643.5273.62963.02572.7253.730(i)Estimate the relationship between GPA and ACT using OLS; that is, obtain the intercept andslope estimates in the equationGPA = B, + B¡ACT.Comment on the direction of the relationship. Does the intercept have a useful interpretationhere? Explain. How much higher is the GPA predicted to be if the ACT score is increased byfive points?(ii) Compute the fitted values and residuals for each observation, and verify that the residuals(approximately) sum to zero.

PLEASE NOTE AS PER THE BARTLEYBY POLICY I AM SOLVING FIRST QUESTION. PLEASE POST ANOTHER QUESTION…

2 In the simple linear regression model y = Bo + Bjx + u, suppose that E(u) # 0. Letting a, = E(u), show that the model can always be rewritten with the same slope, but a new intercept and error, where the new error has a zero expected value.

2 In the simple linear regression model y = Bo + Bjx + u, suppose that E(u) # 0. Letting a, = E(u), show that the model can always be rewritten with the same slope, but a new intercept and error, where the new error has a zero expected value.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter4A: Problems In Applying The Linear Regression Model

Section: Chapter Questions

Problem 2E

See similar textbooks

Related questions

Q: Section 2: Short Essay Questions: 1. A source of constant discussion among applied econometricians…

A: Regressions are used to quantify the link between one variable and the other factors that are…

Q: QNo. 4 growth of Pakistan is facing issues of energy supplies, oil prices volatility and political…

A: Model 1 dependent variable (Y) : GDP 4 independent variables(Xi) : EC, INF, OP, PIS Equation :…

Q: 1 Consider an estimated linear regression model with a response Y and four predictors X1, X2, X3,…

A: Response variable = Y = Annual sales (in $1000s) Predictor variables: = X1 (in $100s) = X2 (in…

Q: State in algebraic notation and explain the assumption about the classical linear regression models…

A: "Regression is the statistical method of analysing the relationship between the dependent variable…

Q: Consider the regression model Yi = β0 + β1X1i + β2X2i + β3(X1i * X2i) +ui. a. ΔY>/ΔX1 = β1 + β3X2…

A: Yi = b0 + b1X1i + b2X2i + ui, i = 1,……..,n Y - dependent variable X1, X2 - two independent…

Q: Which of the following is NOT TRUE in describing the assumptions for the classical linear…

A: It is not necessary for an error term to follow a normal distribution, as OLS does not require it.

Q: Which of the following is an example of a dynamic regression model? OY = Bo + B1Xit + B2X2# + Ut OY:…

Q: What is multicollinearity?Discuss causes and consequences of multicollinearity for OLS estimation.…

A: (a) In a multiple linear regression model which means a regression model with more than one…

Q: Which one of the following statements is true for a linear regression model with non-spherical…

A: Linear regression is maybe one in all the foremost documented and well understood algorithms in…

Q: Suppose the model of interest is Y, A+ BXu+ BX2 + u, where E(uX)-0 and E(u X)= a? and X1 and X2 are…

A: The coefficient estimates will be the same, but the standard error will be smaller in multivariate…

Q: rue or False For a linear regression model including only an intercept, the OLS estimator of that…

Q: Suppose you decide to estimate a student consumption function. After you run an OLS regression on…

A: The regression equation studies the magnitude of relationship between the dependent variable and the…

Q: An online clothing retailer examined their transactional database to see if total yearly Purchases…

A: As per the question, the least square regression model is given as: Purchase^=-33.8+0.019(income)…

Q: 6. The following two regression models are Probit and Logit respectively: P(Y-112)-(B+B₁ × X₁ +₂×…

A: Given function Pr(Y=1|X)=ϕ(β0+β1X1+β2X2)---Probit modelPr(Y=1|X)=F(β0+β1X1+β2X2)---Logit model

Q: All the regression assumptions lie on the residuals, for both simple and multiple regression. True…

A: Not all but some of the assumptions of regression lie on the residuals, for both whether it is…

Q: A company wants to use regression analysis to forecast the demand for the next quarter.In such a…

A: Regression analysis includes the statistical methods used to calculate the relationship between an…

Q: In a simple linear regression equation, if X increases by 3: Select one: a. Y increases by B1 b. Y…

A: Answer to the question is as follows :

Q: The Ipod Touch has been out for several years now and a lot of data has been collected. There is a…

A: The Law of demand refers to the inverse or negative relationship between quantity demanded of goods…

Q: You are interested in the effect of a factory being inspected on whether it reduces its pollution…

A: Introduction This effect of fussy regression can be solved by Cartesian method: number of reported…

Q: Section 2: Short Essay Questions: 1. A source of constant discussion among applied econometricians…

A: Regressions are used to quantify the link between one variable and the other factors that are…

Q: Problem 2 Consider the following regression model: log(y;) = 6o + Bilog(x1:) + B2x2i + B3x3i + u;…

A: The given regression model is expressed as follows:

Q: Let be the residual for observation i for an estimated regression model. If 1.2 and ez = -0.33 R2 is…

A: e1= 1.2 and e2=0.33 Here clearly R^2 is less than 1 and RSS definitely positive.

Q: You are running a probability regression. If your data contains many outliers, you’d be better off…

A: Probability regression is the statistical fitting of an s-curve logistic or logit function to a data…

Q: 1. Can you estimate a regression model for Y and X? 2. What are the assumptions of the model in 1?…

A: According to the answering guidelines, we can answer only three subparts of a question and the rest…

Q: In the multiple regression model, the assumption of no perfect collinearity is best described as:…

A: "Since you have asked multiple questions, we will solve first question for you .. If you want any…

Q: The regression equation to predict sales based on temperature is: Predicted sales = -2419.01+ 98.02…

A: Estimated regression equation is Predicted sales = -2419.01+ 98.02 (temperature)

Q: What is the model constant when the dummy variable equals 1 in the following equations, where x1 is…

A: Dummy variable is the categorical variable that can take only two values; 0 and 1, which describes…

Q: Using a sample from a population of adults, to estimate the effects of education on health, we run…

A: Given regression equation Hypertensioni= α+βeduci+γXi+εiWhere Hypertension= Y is binary…

Q: Question 3 Consider a multiple regression model predicting Calories = 6.53+ 30.84 BMIl + 90.14…

A: Calories=6.53+30.84BMI+90.14Gender+30.94AgeGender=0 if maleGender =1 if female Calories consumed by…

Q: A researcher wants to study the determinants of crime in Turkey. For this she has data 81 Turkish…

A: does not allow covariance between Uit and polpc allows covariance between ai and polpc

Q: According to Environmental Kuznets curve, it is expected that there is an Inverse-U shape…

A: Given: Dependent Variable = Y Independent Variable = X Y represents Air pollution X represents Real…

Q: Suppose you estimate a regression model with 5 explanatory variables and an intercept from a sample…

A: We have sample size of 46, for a small sample size we have to use the student's t distribution.

Q: Given the estimated multiple regression equation ŷ = 6 + 5x1 + 4x2 + 7x3 + 8x4 what is the predicted…

A: Multiple linear regression is used to explain the relationship between two or more independent…

Q: Consider the following bivariate linear regression model y = a+3x+u. Suppose that E[u|x] # 0 and…

A: x : Endogenous variable z: Instrument for x The IV estimate of B = cov(y, z)cov(x, z) = 0.50.5 = 1

Q: consider a regression model Yi=B1+B2Xi+ui and you estimated B2hat =0.3. This implies that a unit…

A: When B2hat = 0.3 Then a unit change in x is predicted to 0.3 unit change in Y.

Q: Based on data from 63 counties, the following model was estimated by least squares:ŷ = 0.58 -…

A: The regression function shows the linear relationship between dependent variable and independent…

Q: Consider the linear regression y; = Bo + B,x, +u, i= 1,..,n,n+1,.,n+ p where E(u,) =0. Is it…

A: Yes it is possible.

Q: QUESTION 5 If the error terms of a linear regression model exhibit heteroscedasticty, which of the…

A: If the error terms of linear model is not homogeneous then we have the problem of…

Q: 6. The following two regression models are Probit and Logit respectively: Pr(Y=1|X)= Pr(Y=1|X)=F(B+B…

A: since you have asked multiple questions and according to policy we can solve only 1 question and for…

Q: Consider the regression model Y; = B1X1¡ + B2X2; + B3 (X1i * X2;) + Uj. Show that (a) AY/AX1 = B1 +…

A: Given:Yi=β1X1i+β2X2i+β3(X1i* X2i) + Ui

Q: When Y is regressed on X, B, > 0, sx# 0, sy# 0, and the fraction of the variation in Y explained by…

A: Note:- “Since you have asked multiple question, we will solve the first question for you. If you…

Q: you are given the following model, where u and v are error terms meeting all standard assumptions of…

A: The value of R square measures how the dependent variables are explained by independent variables.

Q: Define Interpretation of coefficients in polynomial regression models?

A: Polynomial regression models are such that there is only one explanatory variable (X) on the…

Q: XYZ company is interested in quantifying the impact of consumer promotions on the sales of its…

A: Since you have asked multiple questions, we will answer the first three questions for you. If you…

Q: Question 15 When the R2 of a regression equation is very high, it indicates that all the…

A: The regression equation is written as follows: Y = b0+b1X Here, Y is the dependent variable b0 is…

Q: Using a sample of recent university graduates, you estimate a simple linear regression using initial…

A: Estimated regression equation: Starting salary = 3200 + 550 x WAM

Q: Consider the following sample regressions for the linear, the quadratic, and the cubic models along…

A: The regression is a popular statistical tool used in fields like economics, investing and finance to…

Question

2 In the simple linear regression model y = Bo + Bjx + u, suppose that E(u) + 0. Letting a, = E(u),
show that the model can always be rewritten with the same slope, but a new intercept and error, where
the new error has a zero expected value.
3 The following table contains the ACT scores and the GPA (grade point average) for eight college stu-
dents. Grade point average is based on a four-point scale and has been rounded to one digit after the
decimal.
Student
GPA
ACT
1
2.8
21
2
3.4
24
3
3.0
26
4
3.5
27
3.6
29
6
3.0
25
7
2.7
25
3.7
30
(i)
Estimate the relationship between GPA and ACT using OLS; that is, obtain the intercept and
slope estimates in the equation
GPA = B, + B¡ACT.
Comment on the direction of the relationship. Does the intercept have a useful interpretation
here? Explain. How much higher is the GPA predicted to be if the ACT score is increased by
five points?
(ii) Compute the fitted values and residuals for each observation, and verify that the residuals
(approximately) sum to zero.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 14 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.

Similar questions

8. Which of the following best describes the linear probability model? The model is the application of the linear multiple regression model to a binary dependent variable The model is an example of probit estimation The model is another form of logit estimation The model is the application of the multiple regression model with a binary variable as at least one of the regressors OO
d. If the director used these 4 weeks of data to create a linear regression, what does that linear regression formula suggest for this week's forecast of employee appointments? What does the regression analysis suggest in general about employee appointments for Director Very Busy?
Suppose that you had data on the amount of pollution in London every year. Write down the regression equation that you would need to estimate to measure the effect of ULEZ on pollution. Describe carefully what the dependent variable, the independent variable, the unit of observation (time or location), and the main coefficient of interest are. What control variables do you think should be included in this regression?
As an auto insurance risk analyst, it is your job to research risk profiles for various types of drivers. One common area of concern for auto insurance companies is the risk involved when offering policies to younger, less experienced drivers. The U.S. Department of Transportation recently conducted a study in which it analyzed the relationship between 1) the number of fatal accidents per 1000 licenses, and 2) the percentage of licensed drivers under the age of 21 in a sample of 42 cities. Your first step in the analysis is to construct a scatterplot of the data. FIGURE. SCATTERPLOT FOR U.S. DEPARTMENT OF TRANSPORATION PROBLEM U.S. Department of Transportation The Relationship Between Fatal Accident Frequency and Driver Age 4.5 3.5 3 2.5 1.5 1 0.5 6. 10 12 14 16 18 Percentage of drivers under age 21 Upon visual inspection, you determine that the variables do have a linear relationship. After a linear pattern has been established visually, you now proceed with performing linear…
1. Consider a linear regression model y = XB + € with E(e) = 0. The bias of the ridge estimator of 3 obtained by minimizing Q(B) = (y — Xß)¹ (y — Xß) + r(BTB), for some r > 0, is ——(X²X + r1)-¹8 1 (X¹X +rI)-¹3 r -r(XTX+rI) ¹8 r(X¹X+r1) ¹3
What is a linear regression model? What is measured by the coefficients ofa linear regression model? What is the ordinary least squares estimator?
Describe the important characteristics of the variance of a conditional distribution of an error term in a linear regression. What are the implicationsfor OLS estimation?
The Results below show the output of the following model: ?=?0+?1?1+?2?2+? Coefficient St. Error t-ratio Intercept 10.492 0.6655 15.77 ?1 0.0154 0.1889 0.08 ?2 0.1353 0.1889 0.72 Observations 100 ?2 0.985 Correlation matrix: X1 X2 X1 1 X2 0.950 1 Instructions: a. The above results show that the model has the problem of multicollinearity, what are the indicators of multicollinearity that can be identified from these results? b. What are the solutions to rectify multicollinearity?
The table to the right contains price-demand and total cost data for the production of projectors, where p is the wholesale price (in dollars) of a projector for an annual demand of x projectors and C is the total cost (in dollars) of producing x projectors. Answer the following questions (A) - (D). (A) Find a quadratic regression equation for the price-demand data, using x as the independent variable. X 270 360 520 780 The fixed costs are $. (Round to the nearest dollar as needed.) ITTI y = (Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to two decimal places as needed.) Use the linear regression equation found in the previous step to estimate the fixed costs and variable costs per projector. The variable costs are $ per projector. (Round to the nearest dollar as needed.) (C) Find the break even points. The break even points are (Type ordered pairs. Use a comma to separate answers as needed. Round to the nearest integer as…
Only typed answer and please don't use chatgpt otherwise I downvote the answer Assume that the relationship between test scores and the student-teacher ratio can be modeled as a linear function with an intercept of 698.9 and a slope of (-2.28). A decrease in the student teacher ratio by 2 will: A) reduce test scores by 2.28 on average B) result in a test score of 698.9 C) reduce test scores by 2.56 on average D) reduce test scores by 4.56 for every school district PLEASE EXPLAIN WHY C IS CORRECT.
1. You are interested the causal effect of X on Y, B1. Suppose that X, and X2 are uncorrelated. You estimate B1 by regressing Y onto X1 (so that X2 is not included in the regression). Does this estimator suffer from omitted variable bias due to the exclusion of X2? (a) Yes (b) No (c) Maybe 2. Omitted variable bias violates which of the following assumptions: (a) The conditional distribution of u, given X1i X2i, ...Xki has a mean of zero (b) (Xi, X2i...Y;), i = 1, ., n are independently and identically distributed (c) Heteroskedasticity (d) Perfect multicollinearity
1.1 Which of the following is NOT a good reason for including a disturbance term in a regression equation?/ A. To allow for random influences on the dependent variable/ B. To allow for errors in the measurement of the dependent variable/ C. It captures omitted determinants of the dependent variable D. To allow for the non-zero mean of the dependent variable/ 1.2 Consider the equation Y = B1 + B2X2 + u. A null hypothesis of H0: B2 = 0 means that/ A. X2 has no effect on the expected value of Y / B. B2 has no effect on the expected value of Y/ C. X2 has no effect on the expected value of B2 / D. Y has no effect on the expected value of X2/ 1.3 The OLS residuals in the multiple regression model/ A. can be calculated by subtracting the fitted values from the actual values / B. are zero because the predicted values are another name for forecasted values / C. are typically the same as the population regression function errors / D. cannot be calculated because there…