Question

Great Plains Roofing and Siding Company, Inc., sells roofing and siding products to home repair retailers, such as Lowe’s and Home Depot, and commercial contractors, the owner is interested in studying the effects of several variables on the value of singles sold($000). The marketing manager is arguing that the company should spend more money on advertising, while a market researcher suggests it should focus more on making its brand and product more distinct from its competitors. The company has divided the United Stated into 26 marketing districts. In each district it collected information (Please check the Data for Homework on Moodle) on the following variables: volume of sales (in thousands of dollars), advertising dollars (in thousands), number of active accounts, number of competing brands, and a rating of district potential. Please conduct regression analysis and demand estimation (show all five steps and the details), then give the managers some suggestions. (For computing elasticity, assume Adv=8. Number of accounts=30, number of competitors=12, market potential=8) Sales Ad Dollars

Sales	Ad Dollars	Number of accounts	Number of Competitors	Potential
79.3	5.5	31	10	8
200.1	2.5	55	8	6
163.2	8	67	12	9
200.1	3	50	7	16
146	3	38	8	15
177.7	2.9	71	12	17
30.9	8	30	12	8
291.9	9	56	5	10
160	4	42	8	4
339.4	6.5	73	5	16
159.6	5.5	60	11	7
86.3	5	44	12	12
237.5	6	50	6	6
107.2	5	39	10	4
155	3.5	55	10	4
291.4	8	70	6	14
100.2	6	40	11	6
135.8	4	50	11	8
223.3	7.5	62	9	13
195	7	59	9	11
73.4	6.7	53	13	5
47.7	6.1	38	13	10
140.7	3.6	43	9	17
93.5	4.2	26	8	3
259	4.5	75	8	19
331.2	5.6	71	4	9

Answer 1

Answer)

The above diagram shows that the Sales is weakly correlated with Ad Dollars and mildly with Potential, positively correlated with Accounts, and negatively correlated with Competitors. We first build a linear model as function of all variables:

> tt <- read.csv("clipboard",header=TRUE,sep="\t")
> pairs(tt)
> sales_lm <- lm(Sales~.,tt)
> summary(sales_lm)

Call:
lm(formula = Sales ~ ., data = tt)

Residuals:
Min 1Q Median 3Q Max
-19.0906 -5.9796 0.8968 6.5667 14.7985

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 178.3203 12.9603 13.759 5.62e-12 ***
Ad_Dollars 1.8071 1.0810 1.672 0.109
Accounts 3.3178 0.1629 20.368 2.60e-15 ***
Competitors -21.1850 0.7879 -26.887 < 2e-16 ***
Potential 0.3245 0.4678 0.694 0.495
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 9.604 on 21 degrees of freedom
Multiple R-squared: 0.9892, Adjusted R-squared: 0.9871
F-statistic: 479.1 on 4 and 21 DF, p-value: < 2.2e-16

The model is significant, and the covariates Accounts and Potential are significant variables.

The overall elasticity is 40.68815.

> predict(sales_lm,newdata=list(Ad_Dollars=8,Accounts=30,Competitors=12,Potential=8)
+ )
1
40.68815