please answer b and c. 1. Let B₁ and 32 denote the OLS estimators of ₁ and 2 in the regression:yi= Bo + Bixi1 + B2x₁2 + Ui.Let B₁ denote the OLS estimators of B₁ in the regressionyi= Bo + B1x1 + Vi.Let 8₁==1(x₁ - x₁)(Xi2 — X₂) / Σ=1(Xi1 — X1₁)².a) ₁ is the OLS estimator of a slope parameter from what regression model?b) Show that 1(Vi-Bo-Bixi1 - B2x₁2)(x₁₁ - x₁) = 0.c) Prove that B₁ =B₁ + ☎1ß₂. Explain the situations in which omitting x₂ from themodel will NOT bias the OLS estimate of ₁.[Hint. Plug in for Bo=ỹ - B₁x₁-B₂x₂ into (b). Then push through the summationand solve for B₁ to complete the derivation.]

Let β^1 and β^2 denote the OLS estimators of β1 and β2 in the regression:yi=β0+β1xi1+β2xi2+μiLet β1^…

Answered: 1. Let B₁ and 32 denote the OLS…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 76E

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A) A linear regression has a =6 and b=5 what is y predicted as when x=9? B) A linear regression has b=3 and a=4.What is the predicted Y for x=7?
3. The research shows that both X₁ and X₂ are theoretically valid, meaning that they both belong in the true regression relationship. Yi Bo + B₁X1i + B₂X₂i + Ei The researcher decides to estimate two regressions for the sample: Y₁ = Bo + B₁X₁i + Ei Y₁ = Bo + B₂X2i + €₁ Would the estimated regression coefficients for ₁ and ₂ be the same as if the researchers had estimated the true regression relationship? How will the error term compare between models? How will the R-squared values for these two regressions compare to the R-squared of the true relationship? Explain and support your answers with relevant formulas.
Consider the multiple regression model Y₁ = Bo + B₁x1₁j + B₂x2j+B3 x 3j+ €j under the usual assumptions labelled A1, A2, A3, A4, A5, A6. Briefly explain which type of graphs are performed in the analysis of residuals.
You have obtained measurements of height in inches of 29 female and 81 male students (Studenth) at your university. A regression of the height on a constant and a binary variable (BFemme), which takes a value of one for females and is zero otherwise, yields the following result: = 71.0 – 4.84×BFemme , R2 = 0.40, SER = 2.0 (0.3) (0.57) Values in parenthesis are standard errors. (a) What is the interpretation of the intercept? What is the interpretation of the coefficient of the dummy variable? How tall are females, on average? (b) Test the hypothesis that females, on average, are shorter than males, at the 1% significance level.
2. Let kids denote the number of children ever born to a woman, and let educ denotes years of education of the woman. A simple regression model relating fertility to years of education is kids = Bo + Bieduc + u, where u is the unobserved error. (1) What factors are contained in u (Please specify TWO factors)? How are these correlated with level of education? (2) Could you demonstrate, using ONE factor you answered in (1) as an example, that due to its correlation to education, the effect of education on number of kids born to a woman will be biasedly estimated. In particular, given the assumption you make on the correlation between that factor and educ as well as kids, will the coefficient of educ be overestimated or underestimated if directly using the regression model shown? (3) Again, using the factor you utilized in (2), show that what you could do in order to obtain an unbiased estimate of B1?
I have some doubts regarding linear regression. if any 2 variables in X1, X2 AND Y have a positive correlation, then in the linear regression Y = b0 + b1X1 +b2X2 +e, will the sign of b1 and b2 both be positive? will the residuals that we get from linear regression will always be uncorrelated given X?
The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature ( x1 ), the number of days in the month ( x2 ), the average product purity ( x3 ), and the tons of product produced ( x4 ). The past year’s historical data are available and are presented in the following table:regression model is y = -102.7132 + 0.6054X1 + 8.9236X2 + 1.4374 X3 + 0.0136X4 a) Estimate sigma^2b.) Using ANOVA, test for significance of regression using α=0.05. Determine the critical value of the test statistic (2 decimal places only). c.) Using ANOVA, test for significance of regression using α=0.05. Determine the computed value of the test statistic d) Calculate R^2 for the computed regression model. Express your answer as a number less than 1 (NOT in %). e) Calculate R_adj^2 for the computed regression model. Express your answer as a number less than 1 (NOT in %).f) Test the significance of x3 at α=0.05. Determine the value of the test statistic. g)…
We wish to predict the salary for baseball players (y) using the variables RBI (x1x1) and HR (x2x2), then we use a regression equation of the form ˆy=b0+b1x1+b2x2. HR - Home runs - hits on which the batter successfully touched all four bases, without the contribution of a fielding error. RBI - Run batted in - number of runners who scored due to a batters's action, except when batter grounded into double play or reached on an error Salary is in millions of dollars. The following is a chart of baseball players' salaries and statistics from 2016. Player Name RBI's HR's Salary (in millions) Miquel Cabrera 108 38 28.050 Yoenis Cespedes 86 31 27.500 Ryan Howard 59 25 25.000 Albert Pujols 119 31 25.000 Robinson Cano 103 39 24.050 Mark Teixeira 44 15 23.125 Joe Mauer 49 11 23.000 Hanley Ramirez 111 30 22.750 Justin Upton 87 31 22.125 Adrian Gonzalez 90 18 21.857 Jason Heyward 49 7 21.667 Jayson Werth 70 21 21.571 Matt Kemp 108 35 21.500 Jacoby Ellsbury 56 9…
consider the regression model Yi = β0 + β1Xi +ui. suppose you know that β0 = 0. derive a formula for the least square estimator of β1
We wish to predict the salary for baseball players (y) using the variables RBI (x1) and HR (x2), then we use a regression equation of the form yˆ=b0+b1x1+b2x2 HR - Home runs - hits on which the batter successfully touched all four bases, without the contribution of a fielding error. RBI - Run batted in - number of runners who scored due to a batters's action, except when batter grounded into double play or reached on an error Salary is in millions of dollars.
Find the means of X and Y variables and the coefficient of correlation between them from the ff two regression equations: 2Y-X-50 = 0 3Y-2X-10 = 0
Consider the two variable regression model: Y = Bo+P,Edu+ B2EXP21 + u, where Y denotes the average monthly income, Edu denotes the number of years of education, Exp denotes the number of years of experience, and u, denotes the error term. Suppose the researcher wants to test whether the effect of education on average monthly income and the effect of experience on the average monthly income of an individual are the same or not So, the test the researcher wants to conduct is Ho: B = 6, vs. H, f,+P2 The hypotheses can be tested by modifying the original regression equation to turn the restriction into a restriction on a single regression coefficient. Suppose the regression function is modified in the following way: Y, Po+Y,Edu, + B2W +u, where y, =P,-P2 and W, = Edu,, + Exp2i %D Since y, = B, - B2, the test the researcher wants to conduct will now be Ho: y=0 vs. H y0. Let y, and SE(y,), denote the estimated slope coefficient of y, and the standard error of 7, respectively. is .D IS If…

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