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Q1:Part 2 REGRESSION ANALYSIS (a) Run a regression to determine the impact of the 2013 unemployment rate (UnempRate2013) on the per capita income (PerCapitalne) in a county. What is the estimated slope? Explain what this number means in words in terms of the unemployment rate and in terms of per capita income. Also indicate if the relationship is statistically significant at the 10%, 5%, and 1% levels. For this first pass, use homoskedastic standard errors. (b) Re-run the regression from part (a) but this time use heteroskedastic standard errors. Are your coefficients the same as in part (a)? Why? Are your standard errors (of your betas) the same as in part (a)? Why? (c) Run the same regression as in part (b) but now also include the following additional regressors: percentage of the population that is college-educated (Ed5CollegePlusPct), percentage of the population that is black (BlackNonHispanic Pct 2010), and percentage of the population that is Hispanic (Hispanic Pct 2010. Now, what is the estimated impact of unemployment rate in 2013 on per capita income? Also indicate if the relationship is statistically significant at the 10%, 5%, and 1% levels? Make sure that you are using heteroskedastic standard errors. (d) Provide economic/econometric intuition as to why the impact of the unemployment rate's impact on per capita income changed between parts (b) and (c). Note that I am asking you to think about the context (and hence the "story" behind these data). (e) Construct a 95% confidence interval for the slope coefficient on UnempRate2013 found in Part 2(c). Write out your calculations. Clearly indicate how this confidence interval relates to whether UnempRate 2013 is statistically significant or not in this context by relating your answer to your constructed confidence interval. (f) You recall from Part 1 that both the means of per capita income and of unemployment rate in 2013 are quite different across metro and nonmetro areas. You therefore want to explore this in more detail. Run the regression from Part 2(c) using only metro areas in 2013 (i.e., Metro2013--1). [Hint: You need to restrict the data based on a criterion before running the regression.] Now, what is the estimated effect of the 2013 unemployment rate on per capita income and also indicate if the relationship is statistically significant at the 10%, 5%, and 1% levels? Make sure that you are using heteroskedastic standard errors. (g) Now, run the regression from Part 2(c) using only non-metro areas in 2013 (Metro2013--0). [Hint: You need to restrict the data based on a criterion before running the regression]. Now, what is the estimated effect of the 2013 unemployment rate on per capita income and also indicate if the relationship is statistically significant at the 10%, 5%, and 1% levels? Make sure that you are using heteroskedastic standard errors. (h) What did you learn from the comparison between results in parts (f) and (g)? Explain your answer. Note that I again am asking you to think about the context (and hence the "story" behind these data). (i) Return to the full sample. Now, run a regression to determine the impact of changing the percentage of the population which is college educated (Ed5CollegePlusPct) on the per capita income (PerCapitalne) in a county. Include controls for the unemployment rate in 2013 (UnempRate2013), percentage of the population that is black (BlackNonHispanicPet2010), percentage of the population that is Hispanic (HispanicPet2010) and now also include a dummy variable for metro status (Metro2013). Now, what is the estimated impact of percentage with a college education on per capita income? Also indicate if the relationship is statistically significant at the 10%, 5%, and 1% levels? Make sure that you are using heteroskedastic standard errors. (j) It is quite common in econometrics to model income variables nonlinearly. Construct a new variable and call it "logine" or whatever you prefer, where logine-In (PerCapitalne). Provide summary statistics for this new variable. (Hint: Think back to how you constructed summary statistics in Part 1.) (k) Now run a regression model with logine as the dependent variable (and we are also going to start controlling for metro status in addition to the other controls). In other words, the control variables are unemployment rate in 2013 (UnempRate2013) as the main regressor, while also including the other regressors: percentage college educated (Ed5CollegePlusPct), percentage non-Hispanic black in 2010 (BlackNon HispanicPet2010), percentage Hispanic in 2010 (HispanicPct 2010), and metro status in 2013 (Metro2013). Now, what is the estimated effect of UnempRate 2013 in words? Also indicate if the relationship is statistically significant at the 10%, 5%, and 1% levels? Make sure that you are using heteroskedastic standard errors. [Careful not to leave out any variables in your regression specification in STATA] (1) What is the null hypothesis corresponding to the F-statistic as reported in the output for the regression in part (k)? What is the conclusion of the reported F-test? Explain (i.e. Do you reject or fail to reject the stated null hypothesis above and how do you know this?) (m) Construct a 95% confidence interval for the slope coefficient on UnempRate2013 in Part 2(k). As usual, write out your calculations. Clearly indicate how this confidence interval relates to whether UnempRate2013 is statistically significant or not in this context by relating your answer to your constructed confidence interval. (n) Discuss what the standard error of the regression (SER), R-squared and adjusted R-squared in part (k) are telling you in terms of the numbers that you have found. Using what you know about the difference between the two formulas, explain specifically why the R² and R² statistics so similar for this case. (0) Use an F-test to test the joint significance of the additional regressors: Ed5CollegePlus, BlackNon- Hispanic Pct 2010, Hispanic Pct 2010, and Metro2013. Find this test statistic and clearly indicate the conclusions of the test. (p) If you had more time to study this question and/or more or different data, what would you suggest doing next? Propose additional variables to add and/or different specifications to try and give specific reasons why you are suggesting these. Answers will vary for this part of the problem. See Answer
Q2:3 Exercise on Stata [25 pts] To answer this question you are required to use the statistical software Stata. Make sure to create a do file with your code, an automated log file of your answers from that code, and write down in a separate document your answers. You are required to submit all three files (i.e., do file, log file, and Word document) before the due date. Load the dataset nbasal using the bcuse command. The dataset contains data on salaries of NBA players and individual player statistics. 1. What is the structure of the data? (Cross-section, time series, or panel data) [1 pt] 2. How many players are in the data? [1 pt] 3. How many of the players are centers? [1 pt] 4. What is the average years of experience of all players? [1 pt] 5. What percent of players are forwards? [1 pt] 6. Name all dummy variables in this dataset. [1 pt] 7. How many of the guards are not married? [1 pt] 8. What percentage of forwards are married? [1 pt] 9. Plot a histogram of wage. Does the wage variable look symmetrically distributed? Why is it the case? (Note that you don't need to paste your graph into your Word document). [3 pts] 10. Find out the average salary by years of experience [Hint: Combine summarize with the prefix bysort] [2 pts] 11. Generate a variable mean_sal_byexper which equals the average salary of players by years of experience, so that for a given player with 2 years of experience, the variable value will be the average salary for players with 2 years of experience. [Hint: Combine egen with the prefix bysort] [3 pts] 12. Produce a scatterplot of mean_sal_byexper against exper. Make sure exper is on the x-axis. [2 pts] 13. What is the correlation between wage and exper? [2 pts] 14. Create a discrete variable called position which equals 1 if a player is a guard, 2 if a player is a center, and 3 if a player is a forward. Label this variable as "Player's position" [2 pts] 15. Create a pie chart to illustrate the frequency distribution of the variable position. Make sure to include the command that indicates the percentages on each slice. Export the graph as .PDF file. [Hint: You will need to use the plabel (all percent) option in order to display the percentages. In your Word document only give the commands you use]. [3 pts]See Answer
Q3:2- Analysing cross-sectional data, we obtained the output shown below. wage refers to monthly wage in thousands of CZK, female is a dummy variable (for woman = 1, for man = 0), exper refers to year of working experience. How would you interpret the estimated intercept and estimated coefficients for regressors female and wage. See Answer
Q4:Find the p-value for the slope, is Income a good Predictor of Sales?See Answer
Q5:According to the correlation table, who is the best candidate predictor for Sales?See Answer
Q6:Based on the model below, which of the following is an example of data extrapolation?See Answer
Q7:Task 1: Classical two-variable linear regression model (OLS) (30 marks) Collect data on gold prices and the Global Consumer Price Index for the period 2000 - 2022. Data is monthly. (a) Plot the scattergram of gold prices and Global CPI. (b) An investment is supposed to be a hedge against inflation if its price and/or rate of return at least keeps pace with inflation. To test this hypothesis, suppose you decide to fit the following model, assuming the scatterplot in (a) suggests that this is appropriate: Gold price, =B₁ + B₂CPI₂+U₂ (c) Test for station arity. (d) Estimate the above regression model. Obtain the estimates of the parameters, their standard errors, R², RSS, and ESS, etc. (e) Interpret the results. (f) Establish a 95% confidence interval for ₂ and 33. (g) How would you test the assumption of the normality of the error term? Show the tests you use.See Answer
Q8:Task 2: Multiple linear regression analysis (40 marks) Collect monthly data on any four different variables in finance. Countries will be proposed by a module leader for each group individually. (a) Plot the chosen variables for the period 2001-2022. (b) Suggest a model (dependent and independent variables) using the chosen variables. (c) Estimate the regression model. Obtain the estimates of the parameters. (d) Interpret the results.See Answer
Q9:Task 3: The linear regression model assumptions and diagnostic tests (30 marks) (a) Find out whether the variables are highly correlated between each other. (b) Is there serial correlation? (c) Use appropriate tests to find out if the error variance is heteroscedastic.See Answer
Q10:1. (a) For each of the variables, what is the average, the standard deviation, the minimum value, and the maximum value in your data set? (b) What is the number of observations in your data set?See Answer
Q11:3. (a) Fit a simple linear regression (SLR) of savings on income, and report the regression results. (b) Is income a statistically significant determinant of savings at the 10% level? (c) How much of the variation in savings can be attributed to the variation in income? (d) What is the effect on savings of an extra £1,000 of income?See Answer
Q12:6. (a) Fit a simple linear regression (SLR) of Isav on line, and report the regression results. (b) Is line a statistically significant determinant of Isav at the 10% level? (c) How much of the variation in Isav can be attributed to the variation in linc? (d) What is the effect on savings of an increase of 1% in income?See Answer
Q13:7. (a) Fit a multiple linear regression (MLR) of Isav on age, nchild, line, grad and hols, and report the regression results. (b) Which of the regressors are individually significant at the 10% level? And at the 5% level? (c) Carry out a test of the joint significance of the variables age, nchild, grad and hols. Which model do you prefer the SLR model in the previous question, or the MLR model in this question? (d) Carry out a RESET test in the MLR model - is there evidence of functional form mis- specification? (e) Carry out a test for heteroskedasticity in the MLR model - is there evidence of het- eroskedasticity?See Answer
Q14:9. (a) Prepare a table reporting the estimates (and corresponding standard errors) from the re- gressions in questions 3(a), 4(a), 6(a), 7(a) and 8(b). In this table, each column should report the results of one regression including the coefficient estimates, the standard errors (robust if necessary), the standard error of the regression and the R². (b) After running all these regressions, which is your preferred model of household savings?See Answer
Q15:(b) 18 marks Assume that E(lbwght white,male, cigs, lfaminc) = Bo + B₁white + B₂male + ß3cigs + ß4lfaminc The associated linear regression equation in error form is given by Ibwght = Bo + B₁white + B₂male + Bacigs + ß4lfaminc + u. i) Estimate (3) by OLS. Report the estimated regression equation in equation form in the main body of your assignment. Report the estimated coefficients and standard errors to three decimal places. Place the Eviews output in Appendix (b). ii) Based on the output obtained when (3) is estimated by OLS, are the regressors in (3) jointly significant? Briefly explain. iii) Based on the reported p-values, are any of the regressors in (3) individually insignificant at the 10% significance level? Briefly explain. iv) Based on the reported p-values, are any of the regressors in (3) individually insignificant at the 5% significance level? Briefly explain. v) Do the estimated coefficients have the expected sign? Briefly explain in two sentences for each estimated coefficient. vi) Evaluate the explanatory power of your model. vii) Interpret 34. viii) Based on the estimated regression equation, what is the most significant influence on the predicted birth weight of a new born infant? Briefly explain. (2) 3 (2 marks) (2 marks) (2 marks) (2 marks) (4 marks) (2 marks) (2 marks) (2 marks)See Answer
Q16:(c) 10 marks i) Test the joint significance of the regressors white and lfaminc in (3). Conduct the test of joint significance at the 5% significance level. Specify the unrestricted and restricted models. State the null and alternative hypotheses, the form and sampling distribution of the test statistic under the null, the sample and critical values for the test statistic, your decision rule and your conclusion. Place the Eviews output for the restricted model in Appendix (c). ii) Comment on the statement that the race of the mother has no effect on birth weight once we control for family income, the gender of the baby and cigarette consumptions by the mother during pregnancy. (8 marks)See Answer
Q17:(d) 12 marks i) Provide an approximate interpretation of 3. ii) Provide an exact interpretation of $3. iii) Is 3 practically significant? Briefly explain. iv) What is the predicted average birth weight of a male child, born to a white mother, who smokes 20 cigarettes per day and who has a family income of $50,000? v) Derive a 95% confidence interval for B3. vi) Comment on the precision of 33 as an estimate of ß3. (2 marks) (2 marks) (2 marks) (2 marks) (2 marks) (2 marks)See Answer
Q18:#1 Consider the following regression which relates salary and performance for Major League Soccer players. salary =B₁ + B₁games + B₂goals + Bassists + u where salary is the salary paid to a player for the season, games denotes games played, goals is the number of goals scored, and assists is the number of assists scored. The coefficients ₂ and 33 relate to player performance; that is, better players will score more goals and obtain more assists. a) What is the expected sign on B₂? Propose a one-sided hypothesis for this coefficient where the alternative hypothesis is in the expected direction of B₂. b) Propose the hypothesis (both the null and the alternative) that player performance does not matter for the determination of salary. c) Suppose you want to run an F-test for the hypothesis P₁ = 0, B₂ = 0. What is the regression that is run to obtain the SSR of the restricted regression? d) If the error term were heteroskedastic in the regression, would using the usual t-statistic be sufficient to determine statistical significance of a regression parameter? Explain.See Answer
Q19:The variables in your data set are: • sau: household savings from income during the year (in £10,000s); age: the age of the head of the household at the end of the year (in years); • nchild: the number of children (aged 17 and under) in the household at the end of the year; • inc: household income during the year (in £10,000s); • grad: a dummy variable which equals 1 if the head of the household is a graduate and 0 otherwise; and, • hols: the number of holidays taken by the household during the year. 1. (a) For each of the variables, what is the average, the standard deviation, the minimum value, and the maximum value in your data set? (b) What is the number of observations in your data set? 2. (a) Calculate the correlation coefficient between sav and inc. Is there a strong relationship between these two variables? (b) Construct a graph that plots savings (on the vertical axis) against income (on the hori- zontal axis). Does the visual evidence support your answer in part (a)?See Answer
Q20:1. Multicollinearity. Suppose that you postulate a model explaining final exam score in terms of class attendance. Thus, the dependent variable is final exam score, and the key explanatory variable is number of classes attended. To control for student abilities and efforts outside the classroom, you include among the explanatory variables various measures of the student's previous year performance. Someone says, "You cannot hope to learn anything from this exercise because the measures of performance that you included are likely to be highly collinear." What should your response be?See Answer

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