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Elly Lilly of Puerto Rico developed




Elly Lilly of Puerto Rico developed the following regresion model, using time-series;data from the past 33 quarters, for one of its nonprescription cold remedies;S = - 1.04 +.24 Q1 -.27 Q2 where;S = quarterly sales (in thousands of cases) of the cold remedy;Q1 = Lilly's quarterly advertising (in thousands) for the cold remedy;Q2 = competitors' advertising for similar products (in ten thousands);Additional information concerning the regression model;sb1 =.032 sb2 =.070 R2 =.64 se = 1.63 Durbin-Watson (d) =.4995;a. Which of the independent variables (if any) appear to be statistically significant (at the.05 level) in explaining sales of the cold remedy?b. What proportion of the total variation in sales is explained by the regression model?;c. Perform an F-test (at the.05 level) of the overall explanatory power of the model.;d. What conclusions can be drawn from the data about the possible presence of autocorrelation?;e. How do the results in part (d) affect your answers to part (a), (b), and (c)?;f. What additional statistical information (if any) would you find useful in the evaluation to this model?;PROBLEM. 16;General Electric Inc., is seeking to develop a model for forecasting future appliance sales. The company decides to test the following model;St = ? + ?1 At + ?2 Ht + ?3 Lt + ?t;where St is the firm's sales in dollars in period t, At is its advertising expenditures, Ht is an index of new housing starts, Lt is an index of liquid assets holdings by consumers, and ?t is the disturbance term.;a. Develop a hypothesis concerning the sign (minus or plus) of each of the ? parameters, that is, predict whether sales will increase or decrease as the result of an increase in each of the independent variables in the model.;Suppose that the following regression equation was estimated from quarterly time-series data;St = 20.2 + 6.1 At + 4.1 Ht - 3.3 Lt;Additional information includes: n = 20 (sample size, i.e., # of quarters);R2 =.79;Standard errors of the coefficients: sb1 = 2.21,: sb2 = 1.23, sb3 = 1.22;Standard error of the estimate: Se = 25.3;b. Would any of the statistical results appear to be inconsistent with the hypothesis developed in part (a)? What statistical factors might explain any inconsistencies?;c. What additional statistical information would you find useful in the evaluation of this model?;d. What practical difficulties would be encountered in using this model to forecast sales for the next four quarters?;PROBLEM # 17. The following table shows the quantity (Q) of output of calculators and the quantity of labor;L TPl (Q) APl MPl TR MRQ MRPl;0 0 - - 0 - -;1 6;2 16;3 29;4 44;5 55;6 60;7 62;8 62;The price of output is $10 per unit (p = $10 / Q);1) Complete the table;2) Calculate and interpret the output elasticity of labor;when L = 4;3) Calculate and interpret the marginal revenue product of labor (MRP) when p = $10 per calculator and L = 5.;2. Consider the following short-run production function where X = variable input and Q = output.;Q = 6 X2-.4 X3;a. Determine the marginal product function (MPx);b. Determine the average product function (APx);c. Find the value of X that maximizes Q;d. Find the value of X at which marginal product function takes on its;maximum value;e. Find the value of X at which average product function takes on its;maximum value;Determine the returns to scale for each of the following productions functions;a. Q = 50 L + 6 K + 8 L Kb. Q = 8 K2 + 5 L K + 6 K2;c. Q = 50 + 6 L K;d. Q = 5 L + 2 L.5 K.5 + 3 K;2. The Bell South Company manufactures plastic broom and mop holders, and the production function for these holders is expressed as;Q = 100 L.80 K.25;Where, Q = number of plastic holders produced per day;L = labor input in worker-hours per day;K = units of capital input per day;Calculate both the average and the marginal product of labor when;K = 1000 and L = 100.


Paper#28704 | Written in 18-Jul-2015

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