Question

In this problem, you will create and use a dummy variable and the regression procedure to test the hypothesis of independence of two variables. The data in tab 17 (Waiting time) in DS6 represent the time spent waiting in the ER prior to being seen for two groups of patients. One group of patients had true emergencies; the second group had conditions requiring urgent medical attention. Using these data, do the following:

1. Rearrange the data so they can be analyzed using the regression tool in the data analysis add-in in Excel. That is, place the waiting times into a single column next to which you will add the dummy variable described in part b below. (2 points)

2. Add an independent variable that has the values 1 for Emergency and 0 otherwise, i.e., create a dummy variable for type of visit. (2 points)

3. Test the hypothesis that waiting time is independent of the reason for the emergency room admission (i.e., that wait time does not depend on the reason for the visit) using regression in Excel. Report the results of your test and include a copy of the ANOVA table and the table with the regression coefficients from the regression analysis in your report. (6 points) ER waiting times Reason for ER visit Urgent Emergency

ER waiting times
Reason for ER visit
Urgent	Emergency
29	33
30	43
32	26
31	46
22	31
26	40
30	34
38	4
29	30
28	24
29	40
38	32
30	36
43	31
23	45
32	20
25	31
32	42
30	29
32	40
35	34
34	44
29	9
21	25
29	29
31	34
36	28
14	37
31	18
36	38
	29
	48
	36
	49
	28
	39
	34
	37
	34
	42

Answer 1

The data is rearranged in the following Excel sheet:

Reason	Binary	Waiting Time
Urgent	0	29
Urgent	0	30
Urgent	0	32
Urgent	0	31
Urgent	0	22
Urgent	0	26
Urgent	0	30
Urgent	0	38
Urgent	0	29
Urgent	0	28
Urgent	0	29
Urgent	0	38
Urgent	0	30
Urgent	0	43
Urgent	0	23
Urgent	0	32
Urgent	0	25
Urgent	0	32
Urgent	0	30
Urgent	0	32
Urgent	0	35
Urgent	0	34
Urgent	0	29
Urgent	0	21
Urgent	0	29
Urgent	0	31
Urgent	0	36
Urgent	0	14
Urgent	0	31
Urgent	0	36
Emergency	1	33
Emergency	1	43
Emergency	1	26
Emergency	1	46
Emergency	1	31
Emergency	1	40
Emergency	1	34
Emergency	1	4
Emergency	1	30
Emergency	1	24
Emergency	1	40
Emergency	1	32
Emergency	1	36
Emergency	1	31
Emergency	1	45
Emergency	1	20
Emergency	1	31
Emergency	1	42
Emergency	1	29
Emergency	1	40
Emergency	1	34
Emergency	1	44
Emergency	1	9
Emergency	1	25
Emergency	1	29
Emergency	1	34
Emergency	1	28
Emergency	1	37
Emergency	1	18
Emergency	1	38
Emergency	1	29
Emergency	1	48
Emergency	1	36
Emergency	1	49
Emergency	1	28
Emergency	1	39
Emergency	1	34
Emergency	1	37
Emergency	1	34

The regression and ANOVA output is given below

SUMMARY OUTPUT
	Regression Statistics
Multiple R		0.172998361
R Square		0.029928433
Adjusted R Square		0.015449753
Standard Error		8.115000544
Observations		69
ANOVA
		df	SS	MS	F	Significance F
Regression		1	136.1231884	136.1231884	2.067069155	0.155164872
Residual		67	4412.166667	65.85323383
Total		68	4548.289855
		Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept		30.16666667	1.481589617	20.36101381	2.1047E-30	27.20940141	33.12393192	27.20940141	33.12393192
X Variable 1		2.833333333	1.970698417	1.437730557	0.155164872	-1.100197171	6.766863837	-1.100197171	6.766863837