Someone please provide complete calculated solutions and brief summary given the

Question

Someone please provide complete calculated solutions and brief summary given the following info: PoolVac mfg and sells a product called Sting Ray accounts for 65 percent amrket share; competition Howard Industries 18 percent market share. Regression Analysis: Q versus P, MAVG, PH. The Regression equation is Q = 2729 - 10.8P + 0.0214Mavg + 3.17Ph Predicator PCoef Estimate (-10.758) Stand Error (1.330) T-ratio (-8.09) P-value (0.000), Mavg Coef Estimate (0.021420) Standard Error (0.009452) T-ratio (2.27) P-value (0.034) Ph Coef Estimate (3.166) Stand Error (1.344 T-ratio (2.36) P-value (0.028) - In your 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 believes Howard Industries is going to price its automatic pool at $250, and average income in the US is expected to be $65,000. Price elasticity: E^= -10.8(300/1670) E^= -1.94 Income Elasticity: E^= .0214(65,000/1670) E^=.83 Cross-Price Elasticity: 3.17 x 250/1670. Please provide recommendations to the following: The Manager of PoolVac is interersted in generating more CASH FLOWS (revenues) but is uncertain whether a price hike strategy or a price cut strategy will achieve this goal. #1 a) Advise the manager on whether a PRICE HIKE or PRICE CUT is the appropriate strategy to increase total revenue for PoolVac. Clearly explain the ECONOMIC RATIONALE behind your pricing recommendation. b) Suppose the manager want to increase UNITS SOLD of Sting Rays by 4 percent. Recommend a pricing strategy to achieve this target; that is, solve for the REQUIRED PERCENTAGE PRICE INCREASE OR DECREASE to achieve this objective. Clearly show all steps in your calculations and BRIEFLY SUMMARIZE YOUR RECOMMENDATION. #2 Assume your research department has forecast that average household income of pool owners is expected to RISE by 3 percent over the next year. To advise the manager on production planning, calculate THE PREDICTED PERCENTAGE INCREASE OR DECREASE in quantity demanded of Sting Rays as a result of the expected 3 percent increase in income next year. (SHOW ALL STEPS in your calculation) Briefly summarize your calculations. #3 SUppose you learn that Howard Industries is expected to RAISE the price of its pool cleaner (Ph) by 2 percent next period. Holding all other factors CONSTANT, calculate the PREDICTED percentage INCREASE or DECREASE in quantity demanded of Sting Rays as a result of the expected 2 percent hike in the price of pool cleaner (Ph) ssold by Howard Industries. (Show all steps in your calculations). Briefly summarize your calculations. Thanks. R Square Coefficient of determination 96.6 percent, All 3 variables are significantly different from zero at 1 per 1 percent level P at both 1 percent and 5 percent, income is is significantly at 5 percent and Ph is significantly at 5 percent. The signs of the three slope paramenters are consistent with consumer theory: b<negative c>positive indicating Sting Ray cleaners are a normal good as expected and d<negative as should be for complement (PoolVac). The closer the P-value to zero the more significant the variable predictor will be. Since the price has a P-value of value of zero is the most significant, while income Ph has P-value greater han 1 percent but less than 5 percent. We have summarized the reported p_value to evaluate the statistical significance of the three estimated slope coefficients (variables). All 3 estimate slope coefficient are significant at .01 or 1 percent significant level since each of the P-values on theeir t_ratio is less than .05 or 5 percent. Additionally, the price variable is also significant at .01 or 1 percent level since the P-value on its T-ratio is approximately zero. So price is the most significant variable. We can evaluate the fit of the overall sample regression equation vary the coefficient of determination and the P-value on the F-ratio. Therefore I am looking for recommendations/solutions to parts 8, 9 * 10.

Explanation / Answer

Here we have given that the regression equation is,

Q = 2729 - 10.8P + 0.0214Mavg + 3.17Ph

Intercept = 2729

Coefficient of P = -10.8

Coefficient of Mavg = 0.021

Coefficient of Ph = 3.17

Here coefficients of P, Mavg and Ph are known as Slope coefficients.

Interpretation of slope coefficients :

If we fixed P and Mavg then one unit change in Ph will be 3.17 unit increase in Q.

If we fixed P and Ph then one unit change in Mavg will be 0.0214 unit increase in Q.

If we fixed Mavg and Ph then one unit change in P will be 10.8 unit decrease in Q.

Now we can test the hypothesis that,

H0 : B = 0 Vs H1 : B not= 0

where B is population slope for independent variable.

Assume alpha = level of significance = 0.05

Here test statistic follows t-distribution with n-2 degrees of freedom.

Now we have to find p-value for taking decision.

If P-value < alpha then reject H0 at 5% level of signicance otherwise accept H0.

And conclude that given variable is significant.

Here for P :

Test statistic = -8.09

P-value = 0.000

P-value < alpha

Reject H0 at 0.05 level of significance.

Conclusion : The variable P is significant.

For Mavg :

test statistic = 2.27

P-value = 0.034

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : The variable Mavg is significant variable.

For Ph :

Test statistic = 2.36

P-value = 0.028

P-value < alpha

Reject H0 at 0.05 level of significance.

Conclusion : The variable Ph is significant variable.

All these variables we can included in the model.

R Square Coefficient of determination 96.6 percent

Interpretation : It expresses the proportion of variation in dependent variable which is explained by variation in independent variables.

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