Problem #2 - - The table below shows the same actual sales of a Product X sold by Company Y from January to December of 2019, as presented in Problem #1. Month 2-Month Moving Average Forecast-Sales (# of Product X) Actual Sales Absolute Value (# of Product X) of Errors 1,860 2,033 3,556 4,211 6,250 7,990 Jan/19 Feb/19 Mar/19 Apr/19 May/19 Jun/19 Jul/19 Aug/19 Sep/19 Oct/19 Nov/19 Dec/19 Jan/20 10,250 9,850 9,980 9,990 7,895 5,353 - Calculate the 2-month Moving Average Forecast for sales from March/2019 to a) January/2019 and enter them in the table above. b) Calculate the Absolute Value of Error for every forecasted month, from March/2019 to January/2020. Enter those values on the table above. c) Mean Absolute Percent Error (MAPE) for the 2-month Moving Average Forecast you created for Product X from March/2019 to January/2020. - Calculate the Mean Absolute Deviation (MAD), the Mean Squared Error (MSE) and the

5. (i) Show that the chance that an exponentially distributed variable takes on a value below its mean is more than 60% and that the chance that the value will be below half of the mean is almost 40%. (ii) When are exponentially distributed interarrival (service) times reasonable / unrea- sonable for a queuing system?

1.9. (-) If a stock declines 20% in one year and rises 23% in the next, is there a net profit? What if it goes up 20% in the first year and down 18% in the next?

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9. When using logistic regression to look at the effect of level of satisfaction with an educational program on whether a student obtained a job at graduation, including satisfaction as a continuous variable in the logistic regression would provide similar results to which of the following contingency table methods (list all that apply): a. CMH (row 2) with satisfaction as the column variable b. CMH (row 1) c. CMH (row 2) with obtained job as the column variable d. CMH (row 3) Pearson chi-square

6. In the table beloe provides predicted population data about the world and India.RegionPredicted Population (millions)Region:                2035                2050World  :                8,933               9766India   :              1,655.7               1670.1 (d) Calculate the absolute change in the percent of the world population that liives in India between 2035 and 2050. Round your results to one decimal place. (e) The predicted population of India is incresing while the percentage of the world population predicted to live is decresing. How can that happen? Explain in full sentences.

45. Table 1.2 shows the mean annual compensation of construction workers. bab Abor Cesaione TABLE 1.2 Construction Workers' Average Annual Compensation Annual Total Compensation (dollars) Year 1999 42,598 2000 44,764 2001 47,822 2002 48,966 Source: U.S. Bureau of the Census, Statistical Abstract of the United States, 2004-2005. (a) Find the linear regression equation for the data. (b) Find the slope of the regression line. What does the slope represent? (c) Superimpose the graph of the linear regression equation on a scatter plot of the data. (d) Use the regression equation to predict the construction workers' average annual compensation in the year 2008. Tabl

In economics we are often faced with causal problems where the endogeneity arises because of simultaneity. A classic example is that if you are interested in estimating a demand curve, the issue is what you observe in the data are equli- birum and prices and quantity which is not only a function of demand but also a function of supply. In this excercise we will generalize the problem of simultaneity bias. Consider a situation where we are interested in the effect of Ti on Yi, i.e. obtaining a consistent estimate of α. But Yi also effects Ti. Let Xi be some exogenous covariates affecting both Yi and Ti. Let us imagine you have an exogenous variable Z which only effects Ti but does not directly effect Yi. In particular, consider the following structural equations: Yi = αTi+Xi′β+ui (1) Ti = ρYi+Xi′γ+Ziδ+νi (2) where E(ui | Xi,Zi) = 0 and E(vi | Xi,Zi) = 0 (a)  Show why you cannot you use OLS to estimate α consistently in model 1? (b)  Solve for the reduced form equation for Ti…

Question 3. Table 1 shows the mileage and the price of Japanese automobiles. Japanese Car Brands Vehicle Mileage Price (mpg) ($'000) 19 14.944 Mazda MPV V6 Nissan Van 4 Acura Legend V6 19 14.799 20 24.76 Mitsubishi Wagon 4 20 14.929 20 Nissan Axxess 4 Mitsubishi Sigma V6 21 21 Nissan Stanza 4 Mazda 929 V6 8 Nissan Maxima V6 21 22 23 24 25 25 27 28 32 33 34 35 i ii Mean Mileage Toyota Cressida Nissan 240SX 4 Subaru Loyale 4 Mitsubishi Galant 4 Honda Prelude Si 4WS 4 (1) Determine the following: Median Mileage Subaru XT 4 Mazda Protege 4 Honda Civic CRX Si 4 iii Mean Absolute Deviation iv Mean Squared Deviation V Sample Variance vi Sample Standard deviation Subaru Justy 3 Toyota Tercel 4 TABLE 1. Mileage and Price of Japanese automobiles median = Toyota Cressida Nissan 240SX 4 where the following table may be useful: Subaru Loyale 4 Mitsubishi Galant 4 Honda Prelude Si 4WS 4 Subaru XT 4 Mazda Protege 4 Honda Civic CRX Si 4 Subaru Justy 3 Toyota Tercel 4 6972 1 2 SM 5 3 4 5 6 7 8 9 10 11…

4. In multiple regression, why do we prefer our IVs to be uncorrelated with each other (i.e., we want to be 0)?