Suppose you estimate the folilowing regression model: AW E = 696.7 + 9.6 x AGE where AWE is average real weekly earnings and AGE is the age of workers. What is the sample average AWE for a sample average age of 41.6? Round to two decimal places as in %3D 3.14. Type your answer.
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- Consider the regression model Yi = β0 + β1Xi + ui.a. Suppose you know that β0 = 0. Derive a formula for the least squaresestimator of β1.b. Suppose you know that β0 = 4. Derive a formula for the least squaresestimator of β1?The 2008 sales and profits of seven companies were given as follows Firm Sales ($ Billions) Profit ($ Billions) Fiat 5.7 0.27 Honda 6.7 0.12 BP 0.2 0.01 Toyota 0.6 0.04 Apple 3.8 0.05 IBM 12.5 0.46 Phillips 0.5 0.02 The estimated value for the company’s Profit can be estimated using the equation; Y ̂i = α ̂ + β ̂Xi……………………………………………………………………Eqn.1 Where; Y = Companies Profit X = Companies Sales α ̂ and β ̂ are estimated parameters in the model Calculate the sample regression line, where profit is the dependent variable (Y) and sales is the independent variable (X)Past class data has shown that the regression line relating the final exam score and the midterm exam score for students who take statistics from the College of Information Technology and Engineering from Dr. Kalaw is: final exam = 50 + 0.5 × midterm One interpretation of the slope is a. students only receive half as much credit (.5) for a correct answer on the final exam compared to a correct answer on the midterm exam. b. a student who scored 0 on the midterm would be predicted to score 50 on the final exam. c. a student who scored 10 points higher than another student on the midterm would be predicted to score 5 points higher than the other student on the final exam. d. a student who scored 0 on the final exam would be predicted to score 50 on the midterm exam.
- Consider the regression model Yi = β0 + β1X1i + β2X2i + ui. Transform the regression so that you can use a t-statistic to testa) β1=β2.b) β1+aβ2=0.c) β1 + β2 = 1.Consider the following multiple regression Price=118.9+0.594BDR+23.5Bath+0.195Hsize+0.004Lsize+0.095Age−48.5Poor, R2=0.75, SER=41.5 (22.7) (2.56) (8.56) (0.017) (0.00049) (0.315) (10.7) The numbers in parentheses below each estimated coefficient are the estimated standard errors. A detailed description of the variables used in the data set is available here . Suppose you wanted to test the hypothesis that BDR equals zero. That is, H0: BDR=0 vs H1: BDR≠0 Report the t-statistic for this test. The t-statistic is ________ (Round your response to three decimal places)A manufacturer is developing a facility plan to provide production capacity for its factory. The amount of capacity required in the future depends on the number of products demanded by its customers. The data below reflect past sales of its products: Year Annual Sales (number of products) Year Annual Sales (number of products) 1 490 5 461 2 487 6 475 3 492 7 472 4 478 8 458 Use simple linear regression to forecast annual demand for the products for each of the next three (3) years, by using the tabular method to: derive the values for the intercept and slope derive the linear equation plot the linear regression line develop a forecast for the firm’s annual sales for each of the next three years
- A specialist in hospital administration stated that no. of employees in a hospital can be estimated by counting the no. of beds in the hospital .A health care researcher decided to develop a regression model in an attempt to predict the number of employees of a hospital by the no. of beds . 12 hospitals were surveyed and obtained following data. No of Beds. Employees 23 69 29 95 29 102 35 118 42 126 46 125 50 138 54 178 64 156 66 184 76 176 78 225 After obtaining the regression model. Interpret it accordingly based on your understanding .Imagine that you first estimate an OLS regression with a random sample of 100 observations and then re-estimate the same regression with 100 additional observations which are also randomly sampled. What would you expect to happen as the sample size increases? a. standard error decreases b. R-squared increases c. 95 percent confidence intervals get wider d. Sum of squared residuals decreasesShow the graphical form of the econometric error using sample regression line (SRL) and the population regression line(PRL).
- Suppose you have the following data: X Y 3 9 7 45 5 25 2 8 Using OLS methods: estimate the following regression model: Sq root of Yi = Beta0 + Beta1(Xi) + errorSuppose the Sherwin-Williams Company has developed the following multiple regression model, with paint sales Y (x 1,000 gallons) as the dependent variable and promotional expenditures A (x $1,000) and selling price P (dollars per gallon) as the independent variables. Y=α+βaA+βpP+εY=α+βaA+βpP+ε Now suppose that the estimate of the model produces following results: α=344.585α=344.585, ba=0.102ba=0.102, bp=−11.192bp=−11.192, sba=0.173sba=0.173, sbp=4.487sbp=4.487, R2=0.813R2=0.813, and F-statistic=11.361F-statistic=11.361. Note that the sample consists of 10 observations. 1.) According to the estimated model, holding all else constant, a $1,000 increase in promotional expenditures decrease or increase sales by approximately 102,813 or 11,192 gallons. Similarly, a $1 increase in the selling price decrease or increase sales by approximately 813,11,192 or 102 gallons. 2.)Which of the independent variables (if any) appears to be statistically significant (at the 0.05…(Don't accept answers from Chat-GPT)You are estimating the following simple linear regression model: Edui = B0 + B1 MomEdu + ui. Where Edu is the years of schooling of an individual and MomEdu is the years of education of the individual's mother (Note: We might estimate this sort of regression to learn about intergenerational transmission of economic success.) a. Suppose you restrict your sample to individuals with MomEdui = 10 What happens to the OLS estimates? b. Suppose you have two random samples of size 100, both with the same In the first sample, half of the mothers have 12 yearsof education and half have 14 years of education. In the second sample, one quarter of of the mothers have each of 10, 12, 14. and 16 years of education. Does the variance of the OLS estimator differ between the two samples? Explain why or why not. C. Suppose you estimate the above regression using a random sample of 100 observations. Then you find another random sample of 100 with the same as the…