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- A researcher wants to test the relationship between the number of years of formal education received (X) and the average weekly earnings (Y) (measured in hundred dollars). A report released by a government agency suggests that the average weekly earnings of individuals with no formal education is equal to $545. The researcher wants to test whether the average weekly earnings with no formal education is $545 or greater than that. He collects data from a sample of 120 individuals and estimates the following regression function: Y-6.91+2.30X, (1.25) (4.25) where , is the predicted value of the weekly earnings for the individual and the standard errors for the coefficients appear in parenthesis. The f-statistic for the test the researcher wants to conduct will be (Round your answer to two decimal places)T or F A household is frequently used in analyses because more consistent data are usually collected at that level.The models below have been estimated using monthly data for the period 2000: 1-2020: 12. The natural logarithm of the variables used in this model is taken and the transaction is made. D08 is the dummy variable that takes a value of 1 in 2008 and after and 0 in other periods. s.e. indicates the standard error. Comment on the coefficients of variables D08 and (X2t * D08) in the model (3) above.
- 1. Suppose have the sample linear regression function: we Y = B, + B,X, +e,, Bo and B are OLS estimates, prove the following equations hold: Ee, = 0 а. %3D b. Se,x, = 0, x, is the deviation form of Xi EeÝ, = 0 c. d. Y = Y 2. Suppose the sample size n=10, we have the following figures for the sample data: ΣΥ-1110; ΣΧ-1 680; ΣΧY -204200 | ΣΧ31 5400; ΣΥ-133300 The representation of PRF is Y = b, +b,X, +u,, u, O iid N(0,4) The OLS estimates for the SRF is ß, and B a. calculate B, and B with the above figures. b. calculate the standard error of B, and B- c. calculate the determination coefficient: R? d. construct 95% confidence interval for b, and b, respectively. e. conduct hypothesis test: HO: b, =0, H1: b, #0. f. conduct hypothesis test: HO: b, =1, H1: b, #1.Number of Scenario Firms Type of Product Market Model A large city has lots of small shops where people can buy sweaters. Each store's sweaters reflect the style of that particular store. Additionally, some stores use higher-quality yarn than others, which is reflected in their price. Dozens of companies produce plain white socks. Consumers regard plain white socks as identical and don't care about who sells them their socks. The technology for producing socks is widely known, and any reputable person who wanted to start a sock manufacturing business could obtain a loan from a bank to buy the necessary machinery. In a large city, two taxi companies own all the licenses that the city will grant to operate taxis. Consumers don't care which cab company they take-if they decide it's worth taking a cab, they flag down the nearest one. The government has granted the U.S. Postal Service the exclusive right to deliver mail.the unemployment rate for 18- to 34-year-olds was reported to be 10.8% (the Cincinnati Enquirer, november 6, 2012). assume that this report was based on a random sample of four hundred 18- to 34-year-olds. a. a political campaign manager wants to know if the sample results can be used to conclude that the unemployment rate for 18- to 34-years-olds is significantly higher than the unemployment rate for all adults. according to the bureau of labor Statistics, the unemployment rate for all adults was 7.9%. develop a hypothesis test that can be used to see if the conclusion that the unemployment rate is higher for 18- to 34-year-olds can be supported.b. use the sample data collected for the 18- to 34-year-olds to compute the p-value for the hypothesis test in part (a). using a 5 .05, what is your conclusion?c. explain to the campaign manager what can be said about the observed level of significance for the hypothesis testing results using the p-value
- Consider the following regression: Test Score, = 68.12 +2.52Hours Studied, - 0.04Hours Studied? %3D Without studying, an individual would average a test score ofA researcher investigating whether government expenditure crowds out investment estimates a regression on data for 30 countries. I-investment; G-government recurrent expenditure; Y=gross domestic product; all measured in $US billion. P= population measured in million. Standard errors are in parentheses. Î= 18.10 (7.79) R² = 0.99 1.07G + 36Y (0.14) (0.02) She suspects that countries with higher GDP may have more variability in their investment. She sorts the observations by increasing size of gdp per capita (Y)and estimates the regression again for the 11 countries with the lowest gdp(Y)and the 11 countries with the largest gdp(Y). The RSS1 from the first regression is 7186. The RSS2 from the second regresison is 28101. Perform a Goldfeld-Quandt Test at a 5% significance level. a. The test statistic for this test is 0.256 b. The critical value defining the rejection region for Ho is 3.18 c. Is there heterscedasticity? Yes=1 or No-0. The answer is 0We have a random sample of workers from a large firm. In 2017, the firm ran a training program. Some workers did the training program, others did not. The firm now wants to assess the effect of the training on earnings. We use the following model to estimate the effect of a training program on annual earnings in 2018: ln(earn2018)=β0+β1train+β2ln(earn2016)+β3educ+β4exper+u where earn2018 = individual total annual earnings in 2018 in dollars train = a dummy variable that takes the value 1 if the individual worker did the training in 2017 and 0 otherwise earn2016 = individual total annual earnings in 2016 in dollars educ = the individual's years of education exper = the individual's years of experience We find: ln(earn2018)^= 11.672 + 0.041train + 0.821ln(earn2016) + 0.037educ + 0.012exper (5.864) (0.019) (0.258) (0.013) (0.007) n=1278, R2= 0.048 Which of the following is the correct interpretation of the…
- The following relationships between wage (W) and education (EDU) are estimated using a sample of 100 individuals. Excel results are reported below Model 1: W=4.3-0.07 EDU+0.9 EDU2 ; se (4.9) (0.07) (0.03) SSR=0.74; SSE=22.7; SST=23.44; Model 2: W=894-21.96 EDU+0.6 EDU2-75.0 What2+6.5 What3; se (885) (25.54) (0.06) (85.0) (3.2) SSR=0.82; SSE=21.68; SST=22.50; where W is wage and What is the fitted value of W. 1. In Model 1 test the hypothesis that education has no effect on wage 2. Test the adequacy of model W=B1+B2 EDU+B3 EDU?Results of Regressions of Average Hourly Earnings on Gender and Education Binary Variables and Other Characteristics Using Data from the Current Population Survey Dependent variable: average hourly earnings (AHE). Regressor (1) (2) (3) 5.59 5.55 College (X,) 5.57 Female (X2) -2.69 -2.67 -2.67 0.30 0.30 Age (X3) 0.70 Northeast (X4) 0.61 Midwest (Xs) -0.28 South (X) Intercept 12.94 4.49 3.83 Summary Statistics SER 6.40 6.34 6.33 0.180 0.194 0.198 0.193 ok97 0.180 4100 4100 4100 Using the regression results in column (2): On average, a worker eans $ per hour for each year that he or she ages.Construct a 95% confidence interval for the average value of y for the following data. Use x = 25, se = 4.40, and the equation of the regression line, = 16.394 +0.196x. x 14 21 28 9 20 y 17 16 22 19 26 (Do not round the intermediate values. Round your answers to 2 decimal places, e.g. 0.75.) SE(Y25) s