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- Q1 a) Consider the following data on hourly wage rates (Y), labour productivity (Xi) and literacy rate (X2) in a country ABV: Y 90 72 54 42 30 12 XI 3 5 6 8 12 14 16 10 7 4 X2 3 2 Calculate the estimators of the regression Y; = ß1 + B2X2i + B3X3¡ + Hi Test the hypothesis B2 = 0 against the alternative ß2 > 0 at 5% level of significance. Calculate R² and R² and comment on them. i. ii. iii. Construct an ANOVA table and check for the significance of the regression at 5% level of significance. iv.The index of industrial production (IP) is a monthly time series that measures the quantity of industrial commodities produced in a given month. This problem uses data on this index for the United States. All regressions are estimated over the sample period 1986:M1 to 2017:M12 (that is, January 1986 through December 2017). Let Ye=1200 x In(IP/IP-1). Suppose that a forecaster estimates the following AR(4) model for Ye Ŷ=0.749 +0.071Y1 + 0.170Y 2 + 0.216Y 3 + 0.167Y(-4 (0.488) (0.088) (0.053) (0.078) (0.064) The forecaster wants to use this AR(4) to forecast the value of Ye in January 2018, using the following values of IP for July 2017 through December 2017: Date IP 2017:M7 2017:M8 2017:M9 2017:M10 2017:M11 2017:M12 105.01 104.56 104.82 106.58 106.86 107.30 The forecast value is a. The forecast value can not be computed with the given values. O b. 4.104 6.485 Od. 0.787None
- Consider the linear regression model Y; = Bo + ß1X; + U¡ for each i in $10,000) and Y; represents the home size (measured in square feet). We run an OLS regression and get: 1,..., n with n = 1, 000. X; represents the annual income of individual i (measured Bl.n = 43.2, SE(§ .n) = 10.2, Bon = 700, SE(Pom) = 7.4. Suppose that we want to test Ho : B1 = 0 against H1 : B1 >0 at 5% significance level. Assuming that the sample size is large enough, which critical value z should we use? a. z = 1.96 b. z = 1.64 С. z = -1.64 d. z = -1.96The measure of standard error can also be applied to the parameter estimates resulting from linear regressions. For example, consider the following linear regression equation that describes the relationship between education and wage: WAGE: = Bo + B₁ EDUC; + &i where WAGE; is the hourly wage of person i (i.e., any specific person) and EDUC; is the number of years of education for that same person. The residual ₂ encompasses other factors that influence wage, and is assumed to be uncorrelated with education and have a mean of zero. Suppose that after collecting a cross-sectional data set, you run an OLS regression to obtain the following parameter estimates: WAGE;= -10.7+ 3.1 EDUC; If the standard error of the estimate of B₁ is 1.04, then the true value of B₁ lies between grows, you would expect this range to in size. and . As the number of observations in a data setEnumerate the 10 assumptions of the classical linear regression model (CLRM) and discuss its importance in econometrics analysis.
- A regression of average weekly earnings (AWE, measured in dollars) on age(measured in years) using a random sample of college-educated full-timeworkers aged 25–65 yields the following: AWE = 696.7 + 9.6 X Age, R2 = 0.023, SER = 624.1.a. Explain what the coefficient values 696.7 and 9.6 mean.b. The standard error of the regression (SER) is 624.1. What are the unitsof measurement for the SER? (Dollars? Years? Or is SER unit-free?)c. The regression R2 is 0.023. What are the units of measurement for theR2? (Dollars? Years? Or is R2 unit-free?)d. What does the regression predict will be the earnings for a 25-year-oldworker? For a 45-year-old worker?e. Will the regression give reliable predictions for a 99-year-old worker?Why or why not?f. Given what you know about the distribution of earnings, do youthink it is plausible that the distribution of errors in the regressionis normal? (Hint: Do you think that the distribution is symmetric orskewed? What is the smallest value of earnings,…I estimate a multiple linear regression model with three explanatory variables and a sample size of 363 observations. The RSS of this model is 0.428217, the adjusted R squared is 0.453103. When I regress the depended variable on a constant only, I find that the RSS of this simple model is 0.789537 The value of the realized F stat for the test on the significance of the regression is: Select one: Ⓒa. 100.9721 and the null is that all betas except the intercept are simultaneously equal to zero O b. 145.056123 and the null is that the model is in the overall significant for the population statistically at 1% significance level 145.056123 and the null is that all betas are simultaneously equal to zero Gm. My Moodle O c. O d. 145.056123 and the null is that all betas except the interecpt are simultaneously equal to zero O e. 100.9721 and the null is that all betas are simultaneously equal to zero Clear my choiceA researcher wants to study the determinants of crime in Turkey. For this she has data 81 Turkish provinces over 17 years. She estimates by OLS the following regression crmpc = Bo + D; + B1polpc + a;+U where crmpc is the crime rate per head of population, polpc is the number of police officers per 1000 individuals. The parameter D, refers to year fixed effects and is one in yeart and zero for all other years. a, is the unobserved province fixed effect and u, is a random unobservable term (idiosyncratic shock). The First Difference estimator (Check all that apply). Your answer: O allows covariance between u, and polpc does not allow covariance between a, and polpc allows covariance between a, and polpc does not allow covariance between u, and polpc O O
- Mita, the manufacturer of copiers, has been spending increasing amounts of money on radio and television advertising in recent years. An analyst employed by Mita wanted to estimate a simple linear regression of the company's annual copier sales versus advertising dollars. Th regression results included SSE = 12593 and SSR = 87663. What is the coefficient of determination for this regression? 0.874 0.935 0.144 0.126This exercise refers to the drunk driving panel data regression, summarizedin Regression analysis of Drunk Driving (see attachment)a. New Jersey has a population of 8.85 million people. Suppose that NewJersey increased the tax on a case of beer by $2 (in 1988 dollars). Use theresults in column (5) to predict the number of lives that would be savedover the next year. Construct a 99% confidence interval for your answer. b. The drinking age in New Jersey is 21. Suppose that New Jersey loweredits drinking age to 19. Use the results in column (5) to predict the changein the number of traffic fatalities in the next year. Construct a 95% confidence interval for your answer.c. Suppose that real income per capita in New Jersey increases by 3% inthe next year. Use the results in column (6) to predict the change in thenumber of traffic fatalities in the next year. Construct a 95% confidenceinterval for your answer.d. How should standard errors be clustered in the regressions in columns(2) through…The data below represent commute times (in minutes) and scores on a well-being survey. Complete parts (a) through (d) below. Commute Time (minutes), x Well-Being Index Score, y 5 72 105 20 25 35 60 69.2 68.0 67.5 67.1 65.9 66.0 63.8 (a) Find the least-squares regression line treating the commute time, x, as the explanatory variable and the index score, y, as the response variable. ŷ=x+ (Round to three decimal places as needed.) (b) Interpret the slope and y-intercept, if appropriate. First interpret the slope. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. For every unit increase in commute time, the index score falls by (Round to three decimal places as needed.) OB. For every unit increase in index score, the commute time falls by (Round to three decimal places as needed.) 1 D. For an index score of zero, the commute time is predicted to be (Round to three decimal places as needed.) on average. on average. OC. For a commute time…