Regression Problem- Confim my Anwers Please?

Question

Please see the below and my answers-- please let me know if you disagree and also if you know the answers to the 2 questions I don't. Any help is greatly appreciated.

PoolVac, Inc. manufactures and sells a single product called the “Sting Ray,” which is a patent-protected automatic cleaning device for swimming pools. PoolVac’s Sting Ray accounts for 65 percent of total industry sales of automatic pool cleaners. Its closest competitor, Howard Industries, has captured 18 percent of the market.

Using the last 26 months of its sales data, PoolVac wishes to estimate demand for its Sting Ray. Demand for Sting Rays is specified to be a linear function of its price (P), average income for households that have swimming pools in the U.S (MAVG) and the price of the competing pool cleaner sold by Howard Industries (PH). The general linear form of the demand function

Qd = a + b P + c MAVG + d PH.

The attached computer printout presents the regression output from 26 observations (monthly data) on the price charged for a Sting Ray (P), average income of households with pools (MAVG), and the price Howard industries charged for its pool cleaner (PH).

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The printout of part of regression output from Minitab for the empirical demand is below:

Regression Analysis: Q versus P, MAVG, PH

Predictor Coef SE Coef T P

Constant 2728.8 531.7 5.13 0.000

P -10.758 1.330 -8.09 0.000

MAVG 0.021420 0.009452 2.27 0.034

PH 3.166 1.344 2.36 0.028

S = 73.0546 R-Sq = 96.6% R-Sq(adj) = 96.2%

Analysis of Variance

Source DF SS MS F P

Regression 3 3379846 1126615 211.10 0.000

Residual Error 22 117414 5337

Total 25 3497260

Source DF Seq SS

P 1 3327368

MAVG 1 22878

PH 1 29600

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1. An estimated demand equation for PoolVac is:

Qd = 2728.8-10.758P+0.021420M+3.166Ph

2. Evaluate the statistical significance of the three estimated slope parameters using a significance level of .05 or 5 percent (you can either use p-values or do a t-test).Please, explain how you decided each parameter was statistically significant or not.

Since the P values of all 3 variables are within the 5% confidence interval, each variable should be considered as staristically significant in determining the demand of the pool vacuums.

3. What is the exact level of statistical significance for estimated slope parameters on price, average income of household and price of related good? Please, explain how you know.

We should look at the P value for each of the slope parameters and in doing so, we find that price is 100% significant, average income (Mavg) is 96.6% (100-.034) and price of competition (Ph) is 97.2% significant (100-.028).

4. Discuss the appropriateness and/or interpretations of the algebraic signs of the three slope parameters, based on your theoretical expectations. Interpret the numerical values of the three slope parameters in the context of this regression.

5. Now evaluate the overall fit of the estimated (sample) regression equation to the data.

a. What percentage of variability in Qd (linear) is explained by a model? Does it indicate a good overall fit? Please, explain.

b. Verify whether the overall regression equation is statistically significant, another words, verify the goodness of overall fit .What is the exact level of significance for the entire regression equation?

Looking at the F stat which is 211.1, we can say the overall regression equation is significant since the absolute value is large. Also, the P value is 0 so there is no chance that this regression equation doesn’t explain the relationship between the given variables and quantity demanded.

Answer 1

All of your answers are good. To say that the F statistic has a large absolute value is a little vague; one would generally either consult an F table to the appropriate threshold value or just look at the P value in the computer output. On the other hand, it isn't wrong, and if your instructor taught it that way you should leave it in.

Regarding the questions you haven't answered, number 4 refers to the direction of the effects on your dependent variable that come with changes in the independent variables. You should look at your coefficients and consider what would happen if you changed the values in your variables. For example, if the price of the product goes up, demand for the product goes down because of the negative coefficient associated with the price variable. If this seems confusing, try plugging in some different values into the equation and calculating the result. The negative coefficient makes sense, because people are going to be less interested in buying something if its more expensive. The question is asking you to evaluate both the actual effects on demand and the expected effects for each of the variables.

Question 5a refers to the R-squared statistic (R-Sq), which is the percent of explained variability as mentioned in the question. Yours is quite high.