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

Conduct a Multiple Regression.

4. Provide a clear-mathematical and a cogent-managerial interpretation of the beta   coefficient of each of the indicator variables.
5. Conduct an appropriate test to determine whether there is a significant difference in the sales for territories in different regions. Use α = 0.05. State the hypotheses, the test statistic, the decision rule, your decision and conclusion.   
6. Given an advertising expenditure = $50000 and the total bonus paid in each territory = $25000, forecast the expected sales of a territory (a) if it is in the South, (b) if it is the West and (c) if it is in the Midwest.

Answer 1

4. For every additional amount spent on advertising in each territory, sales will increase by 1.5460.

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

For every geographic region in each territory, sales will increase by 118.8992.

5. The hypothesis being tested is:

H0: β3 = 0

H1: β3 ≠ 0

The test statistic is 4.145.

Decision rule: Reject Ho if p-value < 0.05.

The p-value is 0.0005.

Since the p-value (0.0005) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a significant difference in the sales of territories in different regions.

6. (a) if it is in the South,

Sales = $1084.248 (in thousands of dollars)

(b) if it is the West and

Sales = $1203.147 (in thousands of dollars)

(c) if it is in the Midwest

Sales = $1322.047 (in thousands of dollars)

The output is:

	R²	0.920
	Adjusted R²	0.909
	R	0.959
	Std. Error	68.888
	n	25
	k	3
	Dep. Var.	SALES
ANOVA table
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
Regression output				confidence interval
variables	coefficients	std. error	t (df=21)	p-value	95% lower	95% upper
Intercept	-84.2192
ADV	1.5460	0.3061	5.050	.0001	0.9094	2.1827
BONUS	1.1062	0.5727	1.932	.0670	-0.0847	2.2971
REGION	118.8992	28.6875	4.145	.0005	59.2403	178.5581

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