 # 1. This question is worth 40 points-4 points each, except for subpa...

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1. This question is worth 40 points-4 points each, except for subparts (a) and (j), which are worth 6 points each. Use the file "Data for Question 1." This file contains 205 monthly observations (1999-1 to 2016-1) on the following variables: FURN: Retail sales of furniture in the U.S.(seasonally-adjusted, in millions of dollars). U: Civilian unemployment rate (seasonally-adjusted in percentage points). HUC: New residential homes under construction (seasonally-adjusted, in thousands of units). SP: Monthly opening value of Standard and Poor's Index of 500 stock prices. a) Use regression to estimate the following model specification. Report the results of the regression-that is, report your estimates of 80, B1, 82, and 83. FURNt = Bo + B1Ut + B2HUCt-1 + 3SP3MA¹ b) Are the signs of the (estimated) coefficients consistent with your (prior) expectations? Explain. c) Suppose the unemployment rate were to rise by 0.5 percentage points. What is the predicted impact on the monthly furniture sales (FURNt), holding all other factors constant. Be precise. d) Can the following null hypothesis be rejected at the 0.05 level? Explain. Ho:B2=0 e) Use the equation you estimated above to obtain a fitted value of FURN, for September 2015 (2015-9) Compute (and report) the ratio of the in-sample forecast error (FURNt - FURN+) for this quarter to the standard error of the regression (SE). Provide an interpretation of this ratio. f) Prepare a chart (not a table) illustrating actual and fitted values of FURNt for the period 1999-4 to 2016-1. g) Report the value of R² and provide a (precise) interpretation. h) Set up an F-test. Can you reject null hypothesis at the 1 percent (.01) significance level? i) Use the data contained in "Forecast" tab of your spreadsheet to forecast the value of FURNt for 2016-5 and 2016-6. Report your results. 2. This question is worth 35 points-3 points for each part except for subparts (e) and (j), which are worth 5 1/2 points each. You have 132 monthly values of retail sales of floor covering (FCS) in the U.S. beginning in January 2005 (2005-1) and running through December 2015 (2015-12), in millions of dollars, not seasonally adjusted). a) Forecast FCS for March 2016 using a 3-month prior moving average technique. b) Compute root mean square error ( /MSE ) for the in-sample forecast using the same technique as in part (a) above. c) Find the 2-decimal point smoothing constant (a) which gives the best fit for (based on the MSE criterion) for the in-sample forecast using the exponential smoothing technique. (Note: the "damping factor" in Excel is equal to 1 -a). d) How does MSE for the exponential smoothing technique compare to its value for the 3-period prior moving average technique? e) Forecast FCS in January 2016 (2016-1) using the exponential smoothing technique (using the smoothing constant you found in part (c)). f) Estimate and report a linear trend component for the FCS time series using the ordinary least squares (OLS) technique. g) Compare the trend value of your series for September 2008 with its actual value in that month. What factors might account for the difference between the trend value and the actual value of FCS for September 2008? h) Compute a seasonal index using a 12 month centered moving average of the FCS series. Based on your results, would you describe floor covering as a seasonal business? Explain. i) Do an in-sample forecast on FCS sales using the multiplicative time series technique (assume the cyclical component is equal to 1 for every month). j) Use the information contained in following table to perform a forecast of FCS for November and December 2015 using the multiplicative time series technique (Note: you will need to compute a trend component for these months using the equation you obtained in part (f)). Trend Seasonal Cyclical Forecast Month Component Component Component (in millions of US \$) Apr-16 ? Use Apr-15 value 0.997 May-16 ? Use May-15 value 1.002 3. This question is worth 10 points. Over a span of 170 years, the men's world record for the mile run was reduced from 4 minutes and 56 seconds in 1804 to Roger Bannister's 3:59.4 in 1954 to John Walker's 3:49.4 in 1975. Regression analysis was used to fit a linear trend line to the data on world record performances since 1804. The trend function estimated is given by: Time =16.473-.0064Y where Time is the time in minutes and Yis the year. a) According to the equation, the passing of one decade should reduce the record by how many seconds? b) Sebastian Coe's 1981 world record was 3:47.3. Hichman El Guerouj broke the world record in 1999 with a time of 3:43.1.How accurate is the equation's forecast for each of these times? c) What is the predicted world record time for 2016 (Note that, as of March 15, 2016, El Guerouj's record is intact)? Would it be reasonable to use the equation for 2050? Explain. Non-Diet Soft Drinks \$/12-Pack \$9.00 Q =8,100 900P 8,100 12-Packs 4. This question is worth 15 points. Answer the following questions. a) See the diagram above that depicts the demand for non-diet soft drinks. Assume the current price of soft drinks is \$3.58 per 12-pack. Compute point elasticity of demand at the current price. Are soft drink companies maximizing profits from the sale of soft drinks? Explain. b) Soft drink consumption is blamed for health problems such as childhood obesity and diabetes. Several states (including Arkansas) impose a soft drink tax, justified by public health concerns. Suppose a soft drink tax is imposed that raises the price of soft drinks (from the current price of \$3.50) by 8 percent. How successful would the tax be in reducing soft drink consumption? Would it make a difference if the pre-tax price were \$4.89 per 12-pack? c) Which figures stated below is likely to represent each of the following. Give the reasons for your choice in each case. a. Income elasticity of demand for low price cuts of meat; b. Income elasticity of demand for Apple iPads; c. Price elasticity of demand for gasoline -1.6 -0.1 +4.3

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