Question

Health Care Corporation (HCC) sells medical supplies to hospitals, clinics, and physician’s offices. HCC currently markets in three geographic regions of the U.S.: The South, the West, and the Midwest. These regions are divided into many smaller sales territories. HCC’s management is concerned about the effectiveness of a new bonus program. Management wants to know if the bonus paid in the past year was related to the sales. In determining this relationship, they also want to take into account the advertisement expenditure. The data set is below. In this data set, the variables are:

SALES = sales (in thousands of dollars)

ADV = amount spent on advertising in each territory (in hundreds of dollars)

BONUS = total amount of bonus paid in each territory (in hundreds of dollars)

REGION is a variable coded to represent the geographic region as follows:

REGION = 1 if South;    = 2 if West; = 3 if Midwest

SALES	ADV	BONUS	REGION
963.50	374.27	230.98	1
893.00	408.50	236.28	1
1057.25	414.31	271.57	1
1183.25	448.42	291.20	2
1419.50	517.88	282.17	3
1547.75	637.60	321.16	3
1580.00	635.72	294.32	3
1071.50	446.86	305.69	1
1078.25	489.59	238.41	1
1122.50	500.56	271.38	2
1304.75	484.18	332.64	3
1552.25	618.07	261.80	3
1040.00	453.39	235.63	1
1045.25	440.86	249.68	2
1102.25	487.79	232.99	2
1225.25	537.67	272.20	2
1508.00	612.21	266.64	3
1564.25	601.46	277.44	3
1634.75	585.10	312.35	3
1159.25	524.56	292.87	1
1202.75	535.17	268.27	2
1294.25	486.03	309.85	2
1467.50	540.17	291.03	3
1583.75	583.85	289.29	3
1124.75	499.15	272.55	2

1. Develop a multiple regression model to predict sales using the explanatory variables: advertising, bonus, and the region. Be sure to create and include the indicator variables appropriately in the model. State the hypothesized regression model (Use MIDWEST as the base-level group).

2. Estimate and state the estimated regression model. Is it significant at α =0.5? How could you tell?

3. Provide a clear mathematical and a cogent managerial interpretation of the beta coefficient of the variable “BONUS”. At what level is this coefficient significant?

Answer 1

1. The multiple regression model is:

y = -84.2192 + 1.5460*x1 + 1.1062*x2 + 118.8992*x3

2. The hypothesis being tested is:

H0: β1 = 0

H1: β1 ≠ 0

Source	SS	df	MS	F	p-value
Regression	11,49,316.7391	3	3,83,105.5797	80.73	1.08E-11
Residual	99,657.0009	21	4,745.5715
Total	12,48,973.7400	24

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the model is significant.

3. For every additional amount of bonus paid in each territory, sales will increase by 1.1062.

The coefficient significant at α =0.10.