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 region's 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.

1. Describe the economic meaning for the individual independent variables included in the Urgent Healthcare Clinic demand equation.Interpret each estimated coefficient and its impact on the dependent variable (number of patients serviced)?

1. 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).

1. From the regression estimates develop a demand equation for Urgent Healthcare Clinic.Use each coefficient average (at the bottom on Table 1) for the non-price variables to develop the demand equation. (Again, assume that all independent variables are statistically significant in your demand equation computation and the variables P_x, Ad and I are held constant in the development of the demand curve). Q = f(P | P_x, Ad, I)

1. Develop the null and alternative hypothesis for the b₁ coefficient (average price per patient - one-tail test), the b₂ coefficient (average price charged by competition - one tail test) and the b₃ coefficient (advertising variable - two tail test). Briefly describe when it is appropriate to use a one-tail test relative compared to a two-tailed t-test?Use a t-test to determine the level statistical significance for each individual independent variables at the 95 and 99 percent confidence levels.

1. Briefly explain the terminology of the coefficient of determination (R²).If one of the independent variables was found to not be statistically significant, what changes might you perform to the original regression equation?

1. Develop the null and alternative hypothesis and conduct an F-test for the complete set of coefficients in the equation to determine the significance at the 95 and 99 percent levels.

SUMMARY

of

the

OUTPUT

for

the

URGENT

HEALTHCARE

CLINIC

Regression

Statistics

Multiple

R

0.948226547

R

Square

0.899133584

Adjusted

R

Square

0.885684728

Standard

Error

839.1882756

Observations

35

ANOVA

df

SS

MS

F

Significance

F

Regression

4

188329215.7

47082303.9

66.8557694

1.64884E-14

Residual

30

21127108.85

704236.962

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

2.93486381

0.00634506

3402.898568

18974.74118

3402.8986

18974.74118

X

Variable

1

-

P

-43.13833013

10.8664516

-3.9698635

0.00041479

-65.33058494

-20.9460753

-65.33058

-20.9460753

X

Variable

2

-

Px

6.851398997

8.494944815

0.8065266

0.42628708

-10.49759282

24.20039081

-10.49759

24.20039081

X

Variable

3

-

Ad

0.022803572

0.006907087

3.30147451

0.00248972

0.008697418

0.036909726

0.0086974

0.036909726

X

Variable

4

-

I

0.106554043

0.051012565

2.08878036

0.0453132

0.002372487

0.210735599

0.0023725

0.210735599

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

1

6

,

4

7

1

.

8

3

163.81

168.95

2

3

5

,

7

3

8

.

1

1

5

4

,

5

8

6

.

5

4

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

11188.8199

3812.381291

2.9349

Price

(P)

-43.13833

10.8664516

-3.97

Competitor

Price

(Px)

6.851399

8.494944815

0.8065

Advertising

(Ad)

0.02280357

0.006907087

3.3015

Income

(I)

0.10655404

0.051012565

2.0888

Coefficient

of

Determination:

R

2

=

89.91

%

Adjusted

R

2

=

88.57%

F

Statistic

=

66.86

Standard

Error

of

the

Estimate

=

SSE

=

839.19

Observations

=

35