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Econ 661: Assignment 2, Spring 2011;Chapters 4 & 5;Instructions;1.;2.;3.;4.;Study the examples in the notes, chapters, and the student workbook carefully before you attempt the;assignment.;Show work for all solutions, and explain your answers. If you do not show work or explain your;answers, you will not get credit even if the answers are correct.;You may post questions on the Discussion Board. But the respondents are only allowed to provide a;general guidance or reference, and not specific steps as how to solve a problem.;Submit the completed assignment by no later than Monday, Feb 14, 11:55pm (your local time).;1. (10 pts) Asssume the following linear model is used to estimate variable Y;Y = 0 + 1X1 + 2X2 + 3X3 + e;Time-series data on Y, X1, X2, and X3 are employed to estimate the parameters in the model. The;computer output from the regression analysis is shown below;VARIABLE;PARAMETER;ESTIMATE;STANDARD;ERROR of;Estimate;INTERCEPT;945.0;445.25;X1;14.26;5.420;X2;4.10;1.65;X3;25.2;10.5;F-ratio = 125.36;R2 = 0.8412;Observations (n) = 75;a.;What are the degrees of freedom of this model and what is the critical t-value at 5%;significance level?;b. Compute the t-value of each of the parameter estimate and determine whether the;parameter estimate is statistically significant at 5% significance level?;c. Write the estimated regression equation. Suppose X1 equals 4, X2 equals 8, and X3 equals;10. What would be the predicted value of Y based on this regression equation?;d. What is the percent of the total variation in Y explained by this regression model?;2. (12 pts) A manager of a company is required to report to the CEO analysis of salaried;employees. To do this, he selects a random sample of 30 employees of 1000 employees. For each;2;employee, he collects monthly salary, service with the company in months, age of the employee;and gender (1=male, 0=female), and specifies the following multiple regression model.;S = 0 + 1X1 + 2X2 + 3X3 +;Where, S = monthly salary in dollars, X1 = service with the company, X2 = age of the employee;X3 = gender of the employee, and = the error term. The manager expects all the explanatory;variables to have positive impact on the annual salary.;He collected the data below for each sample of employee.;Employee;1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16;17;18;19;20;21;22;23;24;25;26;27;28;29;30;Salary;$1,769;1,740;1,941;2,367;2,467;1640;1756;1706;1767;1200;1706;1985;1555;1749;2056;1729;2186;1858;1819;1350;2030;2550;1544;1766;1937;1691;1623;1791;2001;1874;Service;93;104;104;126;98;99;94;96;124;73;110;90;104;81;106;113;129;97;101;91;100;123;88;117;107;105;86;131;95;98;Age;42;33;42;57;30;49;35;46;56;23;67;36;53;29;45;55;46;39;43;35;40;59;30;60;45;32;33;56;30;47;Gender;1;1;1;1;1;1;1;0;0;0;0;0;0;0;1;0;1;0;1;1;1;1;0;1;1;0;0;0;1;1;Estimate the model using Excel. If you are not familiar with Excel, please follow the;steps below.;3;1.;Input the number of observations (employees) in column A, salary in column B;service in C, age in D, and gender in E. (Hint: you can copy and paste the data to the;Excel spreadsheet);2.;Click on Data, Data analysis at the top right, and on Regression *.;3.;Specify the input range for S as B1: B31, and the input range for service, age, and gender;as C1: F31, or highlight the input ranges for the explanatory variables.;4.;Check the label box and click OK. This will give you a summary Excel regression;output similar to the Excel output shown on page 127 panel B of your text. Copy;and;paste your Excel output here, and answer the following questions using the;regression;summary output.;* If Data Analysis is not available upon clicking Data, click on the Excel icon at the top left, click on;Excel options, click on Add-ins, click on Analysis Toolpak, click on go, check the Analysis Toolpak and;click ok. You will now be able to see Data analysis at the top right when you click on Data.;a.;Determine the statistical significance of each of the independent variables at 5%.;b.;Is this model as a whole statistical significant at 5% level of significance?;c.;Write the estimated regression equation, and explain the contribution of each of;independent variables to the annual salary.;d.;Do all the coefficient estimates have the expected sign? Explain.;e.;What is the predicted average monthly salary of a male employee with 85 months of service;and 56 years old according to this regression model?;3. (6 pts) Assume that an individual consumes two goods: X and Y. The total utility of each;good is independent of the rate of consumption of the other good. The price of X is $40 and the;price of Y is $60. Use the following table of total utilities to answer the following questions.;Units of Good X;1;2;3;4;5;6;Total Utility of X;20;38;54;68;80;90;Units of Good Y;1;2;3;4;5;6;Total Utility of Y;45;78;108;135;159;180;a.;What is the marginal utility per dollar spent on the 5th unit of X?;b.;What is the marginal utility per dollar spent on the 4th unit of Y?;c.;If the consumer has $420 to spend on X and Y, how many units of X and Y should the;consumer buy to maximize total utility subject to this budget constraint?;4;4. (9 pts) Suppose the diagram above represents a consumers budget constraint. Assume the;consumers income is $1,200 per month. Using this income and the information given in the;diagram, answer the following questions.;a.;What are the prices of Y and X at the budget constraint depicted by the line 100Y and 80X?;b.;What is the value of Y2 in the graph above?;c.;What is the price of Y at the budget constraint depicted by the line 150Y and 80X?;d.;What is the value of Y1 in the graph above?;e.;What are the slopes of the budget lines in the graph above?

 

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