Question

Chapter 5

Question 5.1

Sherwin-Williams Company aims to develop a demand model for its line of exterior house paints. The most important variables affecting paint sales (Y) (measured in gallons) are:

Promotional expenditures (A): expenditures on advertising

Selling price (P)

The chief manager decides to collect data on the variables in a sample of 10 company sales regions that are roughly equal in population. Data on paint sales, promotional expenditures are shown in Table 5.1.

The company is interested in developing a multiple regression model with paint sales (Y) as the dependent variable and promotional expenditures (A) and selling price (P as the independent variable.

An estimated regression equation for Sherwin-Williams paint would be specified as follows:

Y = a + b₁A + b₂P.

Table 5.1

Sales region	Sales (Y)	Promotional expenditures (A)	Selling price (P)
1	160	150	15
2	220	160	13.5
3	140	50	16.5
4	190	190	14.5
5	130	90	17
6	160	60	16
7	200	140	13
8	150	110	18
9	210	200	12
10	190	100	15.5

1. Use Excel spreadsheet to run the regression by using information in Table 5.1. Paste your regression results.

2. Based on the regression result in (5.1), find intercept, a, and slope coefficients, b₁ and b₂.

(Please use up to three decimal points)

3. Give an economic interpretation of the estimated slope coefficients, b₁ and b₂.

(Hint: explain how one unit increase in each independent variable influences a dependent variable, when all other things being equal)

4. Explain whether a slope coefficient b is statistically significant at the five percent significance level.

PLEASE SHOW WORK

Answer 1

a.

b. Intercept a = 344.585, b1 = 0.1064, b2 = -12.111
c. Intercept a = 344.585 means even when b1 and b2 are equal to zero, the average sales would be of 344.585 units of house paints
b1 = 0.1064, means with one unit increase in promotional expenditures, there would be 0.1064 units increase in the sales of house paints
b2 = -12.111, means with one unit increase in selling price, there would be 12.111 units decrease in the sales of house paints
d. As the P-value for b1 is greater than 0.05, the slope coefficient for promotional expenditures (A) is not significant at 5 percent level
e. As the P-value for b2 is less than 0.05, the slope coefficient for selling price (P) is significant at 5 percent level