Demand Estimation for the Urgent Healthcare Clinic Consider the hypothetical example of the Urgent Healthcare Clinic (UHC), a chain of urgent care facilities in 35 regional areas across the U S Management of the Urgent Healthcare Clinics has initiated an empirical estimation of customer traffic at their 35 regional locations to help the clinics formulate updates to patient pricing and possible expansion plans for the coming year Annual operating data for 35 regions appear in the attached spreadsheet (Table 1) Regression results also in the spreadsheet (Results Table 2) The following regression equation was fit to these data Q i b 0 b 1 P i b 2 P xi b 3 Ad i b 4 I i u it Where Q is the number of annual patients serviced, P is the average price charged per patient visit (patient amount, in dollars), P x is the average price per patient charged by competing facilities (in $) Ad is the local advertising budget for facilities in each region (in $), I is the average income per household in each regions service area, u i is a residual (or disturbance) term The subscript indicates each of the 35 regional markets (i 1,, 35) from which the observation was taken Least squares estimation of the regression equation on the basis of the 35 data cross sectional observations resulted in the estimated regression coefficients and other statistics as shown in the results and in Table 2 Questions 2 Using the estimates from the regression analysis, compute the expected (average) unit sales and average sales revenue for a typical region (Assume that all independent variables are statistically significant in your computations) SUMMARY of the OUTPUT for the URGENT HEALTHCARE CLINIC Regression Statistics Multiple R 0 9482265466 R Square 0 8991335836 Adjusted R Square 0 8856847281 Standard Error 839 1882756 Observations 35 ANOVA df SS MS F Significance F Regression 4 188329215 7 47082303 93 66 85576941 0 Residual 30 21127108 85 704236 9618 Total 34 209456324 6 Coefficients Standard Error t Stat P value Lower 95 Upper 95 Lower 95 0 Upper 95 0 Intercept 11188 81987 3812 381291 2 934863808 0 006345064316 3402 898568 18974 74118 3402 898568 18974 74118 X Variable 1 P 43 13833013 10 8664516 3 96986355 0 0004147908856 65 33058494 20 94607533 65 33058494 20 94607533 X Variable 2 Px 6 851398997 8 494944815 0 8065266046 0 4262870847 10 49759282 24 20039081 10 49759282 24 20039081 X Variable 3 Ad 0 02280357213 0 006907087145 3 301474507 0 002489724873 0 008697418298 0 03690972596 0 008697418298 0 03690972596 X Variable 4 I 0 1065540431 0 05101256462 2 08878036 0 04531319837 0 002372487454 0 2107355988 0 002372487454 0 2107355988 Table 1 Urgent Healthcare Clinics (35 Markets) Demand Price Competitor Advertising Income Market (Q) (P) Price (Px) (Ad) (I) 1 16,611 199 62 200 52 200,259 54,880 2 16,453 168 20 198 00 204,559 51,755 3 19,201 138 66 142 00 286,647 59,955 4 12,258 218 01 222 30 188,025 52,000 5 18,142 158 00 156 02 287,422 58,491 6 17,973 157 00 158 36 266,224 57,219 7 13,024 208 20 209 15 177,954 48,685 8 15,004 189 01 188 97 200,139 52,219 9 16,254 187 96 187 52 200,215 54,775 10 12,880 222 42 221 27 180,728 54,932 11 16,784 147 94 152 66 206,603 58,092 12 17,468 128 47 129 68 228,620 54,929 13 19,866 118 99 220 00 290,241 56,057 14 17,941 129 72 127 38 252,777 55,239 15 17,707 138 46 138 20 247,300 57,976 16 17,215 148 37 149 43 248,765 59,576 17 17,427 148 36 149 28 249,957 57,454 18 12,320 228 19 220 00 181,317 48,480 19 12,400 208 50 208 38 194,393 50,249 20 15,004 158 34 157 67 205,699 54,696 21 17,581 147 54 149 08 242,270 58,600 22 19,880 129 89 127 10 275,588 60,472 23 14,684 178 76 179 22 200,667 53,409 24 15,468 188 39 189 65 237,816 52,660 25 11,213 228 42 232 00 209,031 50,464 26 18,735 148 82 158 97 269,934 56,525 27 13,830 159 10 158 22 200,921 49,489 28 17,803 149 77 148 96 259,358 49,375 29 19,009 130 07 137 76 288,787 58,254 30 19,213 120 55 128 75 292,270 52,600 31 19,735 118 79 118 99 295,588 54,472 32 13,830 209 50 220 23 187,667 46,409 33 17,803 149 55 149 75 257,816 57,660 34 19,009 123 00 129 99 289,031 60,464 35 16,789 148 91 147 96 246,246 52,017 Mean 16,471 83 163 81 168 95 235,738 11 54,586 54 Table 2 Estimated Demand Function for the Urgent Healthcare Clinic Estimated Standard Error Computed Variable Coefficient of Coefficient t statistic (1) (2) (3) (4) (2) (3) Intercept 11188 81987 3812 381291 2 934863808 Price (P) 43 13833013 10 8664516 3 96986355 Competitor Price (Px) 6 851398997 8 494944815 0 8065266046 Advertising (Ad) 0 02280357213 0 006907087145 3 301474507 Income (I) 0 1065540431 0 05101256462 2 08878036 Coefficient of Determination R2 89 91 Adjusted R2 88 57 F Statistic 66 86 Standard Error of the Estimate SSE 839 19 Observations 35

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Demand Estimation for the Urgent Healthcare Clinic Consider the hypothetical example of the Urgent Healthcare Clinic (UHC), a chain of urgent care facilities in 35

Demand Estimation for the Urgent Healthcare Clinic

Consider the hypothetical example of the Urgent Healthcare Clinic (UHC), a chain of urgent care facilities in 35 regional areas across the U.S. Management of the Urgent Healthcare Clinics has initiated an empirical estimation of customer traffic at their 35 regional locations to help the clinics formulate updates to patient pricing and possible expansion plans for the coming year. Annual operating data for 35 regions appear in the attached spreadsheet (Table 1). Regression results also in the spreadsheet (Results/Table 2).

The following regression equation was fit to these data:

Q_i = b₀ + b₁P_i + b₂P_xi + b₃Ad_i + b₄I_i + u_it.

Where: Q is the number of annual patients serviced,

P is the average price charged per patient visit (patient amount, in dollars),

P_x is the average price per patient charged by competing facilities (in $)

Ad is the local advertising budget for facilities in each region (in $),

I is the average income per household in each regions service area,

u_i is a residual (or disturbance) term.

The subscript indicates each of the 35 regional markets (i = 1,, 35) from which the observation was taken. Least squares estimation of the regression equation on the basis of the 35 data cross-sectional observations resulted in the estimated regression coefficients and other statistics as shown in the results and in Table 2.

Questions

2- Using the estimates from the regression analysis, compute the expected (average) unit sales and average sales revenue for a typical region? (Assume that all independent variables are statistically significant in your computations).

SUMMARY of the OUTPUT for the URGENT HEALTHCARE CLINIC

Regression Statistics
Multiple R	0.9482265466
R Square	0.8991335836
Adjusted R Square	0.8856847281
Standard Error	839.1882756
Observations	35

ANOVA
	df	SS	MS	F	Significance F
Regression	4	188329215.7	47082303.93	66.85576941	0
Residual	30	21127108.85	704236.9618
Total	34	209456324.6

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	11188.81987	3812.381291	2.934863808	0.006345064316	3402.898568	18974.74118	3402.898568	18974.74118
X Variable 1 - P	-43.13833013	10.8664516	-3.96986355	0.0004147908856	-65.33058494	-20.94607533	-65.33058494	-20.94607533
X Variable 2 - Px	6.851398997	8.494944815	0.8065266046	0.4262870847	-10.49759282	24.20039081	-10.49759282	24.20039081
X Variable 3 - Ad	0.02280357213	0.006907087145	3.301474507	0.002489724873	0.008697418298	0.03690972596	0.008697418298	0.03690972596
X Variable 4 - I	0.1065540431	0.05101256462	2.08878036	0.04531319837	0.002372487454	0.2107355988	0.002372487454	0.2107355988

Table 1 - Urgent Healthcare Clinics (35 Markets)

	Demand	Price	Competitor	Advertising	Income
Market	(Q)	(P)	Price (Px)	(Ad)	(I)

1	16,611	199.62	200.52	200,259	54,880
2	16,453	168.20	198.00	204,559	51,755
3	19,201	138.66	142.00	286,647	59,955
4	12,258	218.01	222.30	188,025	52,000
5	18,142	158.00	156.02	287,422	58,491
6	17,973	157.00	158.36	266,224	57,219
7	13,024	208.20	209.15	177,954	48,685
8	15,004	189.01	188.97	200,139	52,219
9	16,254	187.96	187.52	200,215	54,775
10	12,880	222.42	221.27	180,728	54,932
11	16,784	147.94	152.66	206,603	58,092
12	17,468	128.47	129.68	228,620	54,929
13	19,866	118.99	220.00	290,241	56,057
14	17,941	129.72	127.38	252,777	55,239
15	17,707	138.46	138.20	247,300	57,976
16	17,215	148.37	149.43	248,765	59,576
17	17,427	148.36	149.28	249,957	57,454
18	12,320	228.19	220.00	181,317	48,480
19	12,400	208.50	208.38	194,393	50,249
20	15,004	158.34	157.67	205,699	54,696
21	17,581	147.54	149.08	242,270	58,600
22	19,880	129.89	127.10	275,588	60,472
23	14,684	178.76	179.22	200,667	53,409
24	15,468	188.39	189.65	237,816	52,660
25	11,213	228.42	232.00	209,031	50,464
26	18,735	148.82	158.97	269,934	56,525
27	13,830	159.10	158.22	200,921	49,489
28	17,803	149.77	148.96	259,358	49,375
29	19,009	130.07	137.76	288,787	58,254
30	19,213	120.55	128.75	292,270	52,600
31	19,735	118.79	118.99	295,588	54,472
32	13,830	209.50	220.23	187,667	46,409
33	17,803	149.55	149.75	257,816	57,660
34	19,009	123.00	129.99	289,031	60,464
35	16,789	148.91	147.96	246,246	52,017

Mean	16,471.83	163.81	168.95	235,738.11	54,586.54

Table 2 - Estimated Demand Function for the
Urgent Healthcare Clinic

	Estimated	Standard Error	Computed
Variable	Coefficient	of Coefficient	t-statistic
(1)	(2)	(3)	(4) = (2) / (3)

Intercept	11188.81987	3812.381291	2.934863808

Price (P)	-43.13833013	10.8664516	-3.96986355

Competitor Price (Px)	6.851398997	8.494944815	0.8065266046

Advertising (Ad)	0.02280357213	0.006907087145	3.301474507

Income (I)	0.1065540431	0.05101256462	2.08878036


Coefficient of Determination: R2 = 89.91 %

Adjusted R2 = 88.57%

F Statistic = 66.86

Standard Error of the Estimate = SSE = 839.19

Observations = 35