1. You are interested in estimating the following model: Y, = B, + RX; +, . B, and B, are the OLS estimators and û is the residual. Y; represents consumption and X;: income. Both Y; and X; are measured in pounds (£). Σ- Σχ-Γ) = 8.72 ΣΧ. ΣΧ-453Σ-48.1 = 48.1 É(Y, - f)² = 24.94 E(X, - X)² =11.1 ΣΧ-5413 Σ- - 0.0309 n-10 Standard error of B; = 0.28 a) Calculate and interpret B, and B. b) Test the null hypothesis H, : B, =0 against the two-tailed alternative at 5% significance level. c) List and explain the assumptions of the Classical Linear Regression Model. d) Compare the formulas for R-squared and adjusted R-squared. Why is the adjusted R-squared often used in multiple regression analysis?

1. You are interested in estimating the following model: Y, = B, + RX; +, . B, and B, are the OLS estimators and û is the residual. Y; represents consumption and X;: income. Both Y; and X; are measured in pounds (£). Σ- Σχ-Γ) = 8.72 ΣΧ. ΣΧ-453Σ-48.1 = 48.1 É(Y, - f)² = 24.94 E(X, - X)² =11.1 ΣΧ-5413 Σ- - 0.0309 n-10 Standard error of B; = 0.28 a) Calculate and interpret B, and B. b) Test the null hypothesis H, : B, =0 against the two-tailed alternative at 5% significance level. c) List and explain the assumptions of the Classical Linear Regression Model. d) Compare the formulas for R-squared and adjusted R-squared. Why is the adjusted R-squared often used in multiple regression analysis?

Name: could i get some help answering part b, c, d 1. You are interested in
Uploaded: 2024-03-20T06:46:03.000Z
Channel: Bartleby
Description: could i get some help answering part b, c, d 1. You are interested in estimating the following model:Y, = B, + RX; +, .B, and B, are the OLS estimators and û is the residual. Y; represents consumption and X;:income. Both Y; and X; are measured in pou

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 33EQ

See similar textbooks

Similar questions

The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.
Consider the following regression Yi = βXi + ui. Show that (a) the OLS estimator of β is βˆ = (Σ(XiYi))/(Σ(Xi^2)) (b) (Σ(uˆi)/)n = 1/n(Σ(Yi − Yˆi))=/0
Do you think E(y)=β0+β1 ln⁡|x|+ β2ex+β3x3 is a linear statistical model What about E(y)=β0+β1x1+eβ2x2 ?
Consider the following population linear regression model of individual food expenditure: Y = 50 + 0.5X + u, where Y is weekly food expenditure in dollars, X is the individual’s age, and 50+0.5X is the population regression line. Suppose we generate artificial data for 3 individuals using this model. This artificial sample, which consists of 3 observations, is shown in the following table: Answer the following questions. Show your working. (a) What are the values of V1 and V4? (b) Suppose we know that in this artificial sample, the sample covariance between X and Y is 150, and the sample variance of X is 100. Compute the OLS regression line of the regression of Y on X. (Hint: Assume these summary statistics and the OLS regression line continue to hold in parts (c)-(e).) (c) What are the values of V5 and V7?
The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).ŷ = 30 + 0.7x1 + 3x2Also provided are SST = 1200 and SSE = 384.The yearly income of a 24-year-old female individual is _____.
Consider the following simple linear regression model: y = β0 + β1x + u. Using a sample of n observations on x and y, you estimate the model by OLS and obtain the estimates βˆ 0, βˆ 1, and the R-squared of the regression, R2 . Then you scale this sample by a factor of 100, obtain a new sample {xi/100; yi/100} for i = 1, . . . , n, re-estimate the model by OLS, and denote the new coefficient estimates by β˜ 0, β˜ 1, and the new R-squared of the regression by R˜2 . a) Give the expression of β˜ 1 in terms of βˆ 1, and justify your answer.
Q3 Part (A) Where investment (I), government expenditure (G), and gross domestic product (Y) are measured in US$ billion and ̂u is the regression residualIs there any problem of Hetroscedasticity in above model? How do you know?
1. Suppose that the sales of a company (Y) is regressed on advertising expenditure (x) and labor cost (z), and the estimated regression equation is Y = 5 + 0.5x + 0.7z + u (where u is the error term). Here, sales, advertising expenditure and labor cost are measured in million Tk. Standard error for the coefficient of x is 0.4, standard error for the coefficient of z is 0.01, and the sample size is 20. Based on this information, find out whether labor cost is a statistically significant variable using an appropriate statistical test.
5.- The following sample represents the two data on chlorine residues (in part per million) in a swimming pool at various times (hours) after the water has been treated with chemicals. Time X024681012 Waste And2.21.81.51.41.11.10.9 a) Calculate a linear regression model for this data. b) Use the model to estimate the chlorine residue in the pool 8 hours after treating it with chemicals. Why is your answer somewhat different than the 1.1 parts per million that was actually observed at 8 hours?
3. The following Table gives data on output per hour (X) and real compensation per hour (Y) for the business and nonfarm business sectors of the U.S. economy. Year 1990 Y X 1991 1 10 1992 3 15 4 20 Estimate the slope of the OLS regression of Y on X (ẞ2) from the following regression: Yi = β₁ + β2 Xi + Ui
Consider the following log-wage regression results for women (W) and men (M) where wages are predicted by schooling (S) and age (A). wW = 2.23 + 0.077Sw + 0.017Aw and wM = 2.33 + 0.0745SM + 0.026AM. Sample means for the variables by gender are: women average a logged wage of 3.90, 12.7 years of schooling, and 40.8 years-old; men average a logged wage of 4.53, 14.2 years of schooling, and 43.9 years-old. Decompose the raw difference in average logged wages using the Oaxaca-Blinder decomposition. Specifically, decompose the raw difference into the portion due to differences in schooling, differences in age, and the portion left unexplained, possibly due to gender discrimination.
How will you choose between following non-nested competing models:- Md=Beta lag (0)+ beta lag(1) Y+ V and Md= alpha lag(0) + alpha lag(1) i+ U