For this exercise, you will take five data points and calculate the coefficients of the bivariate...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
For this exercise, you will take five data points and calculate the coefficients of the bivariate regression model by hand. This is not something you would typically do, but by doing so, I hope the relevant concepts will become more concrete. You will complete this exercise using 5 data points (n = 5) which are combinations of values of a Y variable and an X variable as indicated: i Y 1 2 3 2 1 4 7 1 5 1 So for instance: Y1 = 1 and X1 = 0. If it helps, I had in mind the idea that Y indicates the number of college applications sent and X is an indicator (dummy) variable for female. There are a few pieces to this problem outlined below: a) Use the formulas for the bivariate regression coefficients to calculate the coefficients a and ß in the regression model: Yi = a – BXi + ei The basic formulas are: B = Cov(Yi, Xi) /Var(Xi) and: 3. a = E[Yi] – BE[Xi] where you can find how to calculate the covariance, variance, and expectation in any resource about statistics. b) Find the difference in mean the mean value of Yi for individuals with Xi = 1 instead of Xi = 0. This should be the same as your coefficient B. C) Copy the table above and extend it by including columns for the fitted value of Yi and the resulting residual for Yi , and residual squared for Yi as well as three additional columns described below. d) Calculate the residual and the residual squared for each observation based on a value of B either one greater than or 1 less than the value of B you calculated. (If you found B = 8 then calculate the fitted values, residuals, and residuals squared based on B = 7 or ß = 9). Verify that the sum of squared residuals from the correct ß is less than the sum of squared residuals from this incorrect B. For this exercise, you will take five data points and calculate the coefficients of the bivariate regression model by hand. This is not something you would typically do, but by doing so, I hope the relevant concepts will become more concrete. You will complete this exercise using 5 data points (n = 5) which are combinations of values of a Y variable and an X variable as indicated: i Y 1 2 3 2 1 4 7 1 5 1 So for instance: Y1 = 1 and X1 = 0. If it helps, I had in mind the idea that Y indicates the number of college applications sent and X is an indicator (dummy) variable for female. There are a few pieces to this problem outlined below: a) Use the formulas for the bivariate regression coefficients to calculate the coefficients a and ß in the regression model: Yi = a – BXi + ei The basic formulas are: B = Cov(Yi, Xi) /Var(Xi) and: 3. a = E[Yi] – BE[Xi] where you can find how to calculate the covariance, variance, and expectation in any resource about statistics. b) Find the difference in mean the mean value of Yi for individuals with Xi = 1 instead of Xi = 0. This should be the same as your coefficient B. C) Copy the table above and extend it by including columns for the fitted value of Yi and the resulting residual for Yi , and residual squared for Yi as well as three additional columns described below. d) Calculate the residual and the residual squared for each observation based on a value of B either one greater than or 1 less than the value of B you calculated. (If you found B = 8 then calculate the fitted values, residuals, and residuals squared based on B = 7 or ß = 9). Verify that the sum of squared residuals from the correct ß is less than the sum of squared residuals from this incorrect B.
Expert Answer:
Related Book For
Microeconomics An Intuitive Approach with Calculus
ISBN: 978-0538453257
1st edition
Authors: Thomas Nechyba
Posted Date:
Students also viewed these programming questions
-
In this exercise you will prove Theorem 9.8.2. a. Prove that the joint p.d.f. of the data given the parameters 1, 2, and can be written as a constant times b. Multiply the prior p.d.f. times the...
-
Calculate the coefficients of correlation for each pair of independent variables in Exercise. What do these statistics tell you about the independent variables and the t-tests of the coefficients?
-
In this exercise, you will define language four, an extension of language three. Here is a sample program in language four, showing all the new constructs: let val fact = fn x => if x<2 then x...
-
Let S be the portion of the cylinder y = e x in the first octant that projects parallel to the x-axis onto the rectangle R yz : 1 y 2, 0 z 1 in the yz-plane. Let n be the unit vector normal to S...
-
Suppose that natural real GDP is constant. For every 1 percent increase in the rate of inflation above its expected level, firms are willing to increase real GDP by 2 percent. The output ratio is...
-
An argon ion laser emits light at 532 nm. What is the frequency of this radiation? Using Figure 6.4, predict the color associated with this wavelength. Wavelength (m) 10-11 -5 10 10-1 10 103 Gammal...
-
What is the basic principle used in Rayleigh's method?
-
Wolford Department Store Is located In midtown Metropolis. During the past several years, net income has been declining because suburban shopping centers have been attracting business away from city...
-
As discussed there are different interview styles that dictate how an investigator will seek information. One effective theme or style is for the investigator to sympathize with the suspect. In the...
-
Review the calculations for The Diamond Ridge Golf Course example discussed in the chapter. 1. Based on these calculations, is there any good-will value? If so, how much? 2. How did you make this...
-
Some questions allow you to interact indirectly with a graph by manipulating a corresponding table of entries. In this type of question, you will not be graded on the final appearance of the graph,...
-
What is the relative significance of relative and absolute brain size in trying to understanding the evolution of brain and behavior?
-
According to a Labour Force Survey in a country, total employment increased by around 1.35 million workers between 2014 and 2020, but the number of unemployed workers increased by 350,000. a. How are...
-
What are the two primary modes of speciation?
-
What is the cerebrum and how is it anatomically organized?
-
What is taxonomy?
-
Consider two local banks. Bank A has 99 loans outstanding, each for $1.0 million, that it expects will be repaid today. Each loan has a 7% probability of default, in which case the bank is not repaid...
-
F.(3e* -2x 3 sin(2x)) is equal to 2 3 Cos 8. IT 3, t (4+@ 2 3, 1+o 1 4 Cos 4 4 1 3. 1 +4cos V7 (1+o 4 1 4 Cos 4 1+0 4-
-
I hate grits so much that the very idea of owning grits makes me sick. I do, on the other hand, enjoy a good breakfast of Coco Puffs Cereal. A: In each of the following, put boxes of grits on the...
-
The tax analyzed in exercise 3.15 is a proportional wage tax. The U.S. federal income tax, however, is progressive. This means that the average tax rate one pays increases the more wage income is...
-
Uncle Vern has just come into some money $100,000 and is thinking about putting this away into some investment accounts for a while. A: Vern is a simple guy so he goes to the bank and asks them...
-
Why is a third-party payer a problem? Private insurance companies are third-party payers, and yet they want to maximize profit. So wouldnt they ensure that the allocation of dollars was efficient?
-
Analyze the following solutions to the problem of Social Security. a. The retirement age is increased to 70. b. The FICA tax is increased. c. Income plus Social Security payments cannot exceed the...
-
Oregon proposed a solution to the health care costs problem that was widely criticized. Under this solution, the state paid only for common medical problems. Special and expensive problems would not...
Study smarter with the SolutionInn App