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Regression Analysis: Q versus P, MAVG, PH The regression equation isQ = 2729 – 10.8 P + 0.0214 MAVG + 3.17 PHP5.13 0.0001.330 -8.09 0.0002.27 0.0342.36 0.028R-Sq(adj) = 96.2%Analysis of VarianceP3 3379846 1126615 211.10 0.000533725 3497260Seq SS1 33273682287829600Consulting Report GuidelinesIn your role as economic analyst for PoolVac, Inc., you must write a (typed) report addressing the following issues relating to the analysis of regression results and the applications of the estimated demand equations and demand elasticities. Your report (case) should be readable and understandable by a third party (such as PoolVac management) that does not have the project instructions or regression results.Introduction•Start your consulting report with an introduction that includes a brief statement of objectives of the report, focusing on your role as consultant to Pool Vac. Then move on to the two major sections of the report:The Estimated Demand Equation and Diagnostic ChecksRecommendations on Pricing, Cash Flows, and ProductionThe Estimated Demand Equation and Diagnostic Checks•Start this section with a brief discussion of the general linear demand equation (recopied here from on p. 1) that will be estimated:Qd=a + b P + c MAVG + d PH.oDefine each of the variables (underneath the demand equation) in the context of this case, then briefly discuss the expected or predicted signs of each the three slope parameters based on demand theory and/or your economic intuition in this specific market of this case. •Describe the sample (data) used to estimate the general demand function.•Then report the estimated general demand equation for PoolVac’s Sting Ray obtained from the regression analysis (copied from the computer output):Qd= 2729 – 10.8 P + 0.0214 MAVG + 3.17 PHVariable(Predictor)Coefficient EstimateStandard ErrorT-ratioP-valuePMAVGPHImportant: before you address the numbered topics below, be sure you have completed the analysis in the bullets above the table (starting on the prior page).1. Complete the typed table above using the regression output on the prior page. This table summarizing the major regression results of your study. (Give the table a title.)2. Now, use the reported p-values in your table to evaluate the statistical significance of the three estimated slope coefficients (variables). Your discussion should address the following questions or issues:•Which variables (estimated slope coefficients) are significant at the .05 or 5 percent significance level? Are any variables (estimated slope coefficients) significant at .01 or 1 percent level? Be sure to explain precisely how you decided the estimated slope coefficients (variables) were statistically significant or not. Which of the three variables (estimated slope coefficients) is the most significant and why? (See the note below.)Note: all analyses in the section above are based on p-values. The p-value approach compares the reported p-values on the t-ratios to the chosen significance level. (So be sure to review the decision rule for the p-value approach.)3. Evaluate the overall fit of the sample regression equation to the data. A complete discussion should address the following:•Report the coefficient of determination (R2), and interpret the value of R2 in the context of this specific regression equation (dependent variable).•State whether the overall sample regression equation is significant at the 5 percent significance level and explain how you decided.4. Discuss the interpretations of the algebraic signs and the numerical values of each of the three slope coefficients (parameters). Your discussion should address the following questions or issues:•Are the algebraic signs of the three slope coefficients consistent with your prior expectations based on consumer demand theory? (Explain for each slope sign.)•Interpret the numerical values of each of the three estimated slope parameters in the context of this specific regression (case).Recommendations on Pricing, Cash Flows, and ProductionIn your job as economic analyst at PoolVac, you must use your regression results to advise the manager at PoolVac make a series of pricing and production decisions. 5. The manager of PoolVac, Inc. believes Howard Industries is going to price its automatic pool at $240, and average income in the U.S is expected to be $60,000. Based on this information, solve for the estimated (simple) demand function and the inverse demand function. Show all work (all steps in your derivations).
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