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- A researcher has a sample of 6 annual observations {94, 104, 102, 99, 111 and 107} for the CPI in country Z for the period 2015 to 2020, and wants to forecast CPI for the years 2021, 2022 and 2023. The researcher uses 3 different forecasting models: A, B and C. Model A is an AR(1) model with no drift and with an estimated autoregressive coefficient = 0.7. Model B is a MA(1) model with no constant and with an estimated MA coefficient = -0.4 (note the minus !). Model C is a random walk model with no drift. The error terms over the 2015-2020 period were estimated to have the values: {3, -1, 2, 4, -3, 1}. a. Compute the 2021, 2022 and 2023 forecasted values for the consumer price index based on the three models. Show the formulas and the details of your calculations, and explain all the related symbols. b. Suppose that the actual values of the CPI over the 2021, 2022 and 2023 were {108, 114, 105}. Calculate the Root mean square error of the three model forecasts over the 2021-2023…You estimate the following regression: In(Earn) = 5.349 + 0.0159*Education (2.755) (0.0092) What is the 99% confidence interval for the effect that an increase in education by 3 years has on earnings? OI-0.24%, 0.12%] OI-0.0078%, 0.040%] OI-0.78%, 3.96%] OI-0.64%, 10.18%] OI-2.35%, 11.89%]An analyst working for your firm provided an estimated log-linear demand function based on the natural logarithm of the quantity sold, price, and the average income of consumers. Results are summarized in the following table: SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Regression Residual Total Intercept LN Price LN Income df 0.968 0.937 0.933 0.003 30 SS MS F 2 0.003637484 0.001818742 202.48598 0.000242516 8.98206E-06 27 29 0.00388 Coefficients Standard Error 0.57 0.00 0.13 0.51 -0.08 0.15 t Stat 0.90 -19.50 1.13 P-value 0.37 0.00 0.27 Significance F 5.55598E-17 Lower 95% -0.65 -0.09 -0.12 How would a 4 percent increase in income impact the demand for your product? Demand would increase by 60 percent. Demand would increase by 0.6 percent. Demand would decrease by 60 percent. Demand would decrease by 0.6 percent. Upper 95% 1.68 -0.07 0.41
- Disposable income, the amount left after taxes have been paid, is one measure of the health of the economy. Using U.S. Energy Information Administration data for selected years from 2015 and projected to 2040, the U.S. real disposable income per capita (in dollars) can be approximated by the equation I = 707.6t + 39,090 where t is the number of years after 2015. (a) What t-value corresponds to 2021? t = (b) Find the predicted U.S. per capita real disposable income (to the nearest $10) in 2021. $ (c) In what year is the U.S. per capita real disposable income expected to exceed $55,000? Extreme Protection, Inc. manufactures helmets for skiing and snowboarding. The fixed costs for one model of helmet are $6600 per month. Materials and labor for each helmet of this model are $55, and the company sells this helmet to dealers for $85 each. (Let x represent the number of helmets sold. Let C, R, and P be measured in dollars.) (a) For this helmet, write the function for monthly total costs…Imagine you are an economist working for the Government of Econville. You are tasked with developing a model to predict the GDP of the country based on various factors such as interest rates, inflation, unemployment rate, and population growth. You collect quarterly data for the past 20 years and start building your model. After running your initial regression, you notice some peculiar patterns in the residuals: (1) residuals do not have identical variances across different levels of the independent variables; (2) two or more independent variables in a regression model are highly correlated with each other; (3) the correlation of a variable with its own past values. You suspect that your model might be suffering from 3 potential issues in the regression analysis that can affect reliability and validity. List 2 factors in your model that might be causing the Multicollinearity and give a reasonSuppose the relationship between the government's tax revenue (T) and national income (Y) is represented by the equation T=10+0.25Y. Plot this relationship on a scale diagram, with Y on the horizontal axis and T on the vertical axis. Interpret the equation.
- The Company purchased a lot for P250k on which they will construct a building with 3 estimates tabulated below. Determine which alterative should be selected using Benefit Cost Analysis at 10%: Building Height 4 stories 8 stories 12 stories Cost of Building P650k P1.5M P2.4M Resale Value at the end of 30 yrs 350k 720k 1M Net Annual Income 120k 250k 340k What is the value of B-C of the 4 story. a. P62,656.413 b. P26,656.413 c. P276,656.413 d. P6,656.413Imagine you are an economist working for the Government of Econville. You are tasked with developing a model to predict the GDP of the country based on various factors such as interest rates, inflation, unemployment rate, and population growth. You collect quarterly data for the past 20 years and start building your model. After running your initial regression, you notice some peculiar patterns in the residuals: (1) residuals do not have identical variances across different levels of the independent variables; (2) two or more independent variables in a regression model are highly correlated with each other; (3) the correlation of a variable with its own past values. You suspect that your model might be suffering from 3 potential issues in the regression analysis that can affect reliability and validity. what are the implications of Heteroscedasticity if this potential issue in your model?The world's population living in extreme poverty has declined linearly between the years 2005 and 2011. In 2005, the percentage of the world's population living in extreme poverty was 20.70% and in 2011, the percentage of the world's population living in extreme poverty was 13.70%. Determine a linear equation that models the world's population in extreme poverty, in percentage, as a function of years since 2005. What is the slope of this function, and what does it tell you in practical terms? Round your answer to the nearest hundredth (0.01). Om = -7.00. The world's population in extreme poverty decreased by 7 percent per year between the years 2005 and 2011. Om = 7.00. The world's population in extreme poverty increased by 7 percent per year between the years 2005 and 2011. Om = 1.17. The world's population in extreme poverty increased by 1.17 percent per year between the years 2005 and 2011. Om = -1.17. The world's population in extreme poverty decreased by 1.17 percent per year…
- (b) The following OLS regression results and White Heteroscedasticity Test are obtained from Eviews for the following regression model C, = B% +ß1Yd + B,Wi + B•IR + Ei. where C = real consumption expenditure Yd = real disposable personal income W = real wealth IR = real interest rate Dependent Variable: CONS Method: Least Squares Sample: 1947 2000 Included observations: 54 Variable Coefficient Std. Error t-Statistic Prob. C -20.71811 12.83272 -1.614476 0.1127 YD 0.733991 0.013758 53.34991 0.0000 0.002484 2.307678 0.0000 0.0204 W 0.035985 14.48563 -2.394320 IR -5.525320 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) Mean dependent var S.D. dependent var Akaike info criterion 0.999401 2888.296 0.999365 1500.920 37.81573 71501.48 -270.7119 10.17451 Schwarz criterion 10.32185 Hannan-Quinn criter. 10.23133 27814.08 Durbin-Watson stat 1.310017 0.000000 Heteroskedasticity Test: White F-statistic Obs*R-squared Scaled explained SS…With a new chef and a creative menu, Café Venetian has witnessed a huge surge in sales. The following data show a portion of daily sales (in $) at Café Venetian in the first 100 days after the changes. Day Sales 1 226 2 185 100 1,737 pictureClick here for the Excel Data File a-1. Estimate the exponential trend model. (Negative values for regression coefficients should be indicated by a minus sign. Round your answers to 2 decimal places.) Predictor Variable Constant Day Coefficient 0.00 a-2. Use the estimated model to forecast for the 101st day. (Do not round coefficient estimates. Round final answer to 2 decimal places.) Forecast for the 101 day2. Question 2: Suppose that you estimate a model of the aggregate annual retail sales of new cars that specifies that sales of new cars are a function of real disposable income, the average retail price of a car adjusted by the consumer price index, and the number of sports utility vehicles sold (you decide to add this independent variable to take account of the fact that some potential new car buyers purchase sports utility vehicles instead). You use the data (annual from 2000 to 2014) and obtain the following estimated regression equation: CARS, = 1.32 + 4.91Y D; + 0.0012 PRICE, - 7.14 SUV (2.39) (0.00045) (71.40) 1 where CARS = new car sales (in hundreds of thousands of units) in year t, YD; = real disposable income (in hundreds of billions of dollars), PRICE = the average real price of a new car in yeart (in dollars), SUV = the number of sports utility vehicles sold in year t (in millions). You expect the variable YD to have a positive coefficient and the variables PRICE and SUV to…