Question

Dr. Lillian​ Fok, a New Orleans​ psychologist, specializes in treating patients who are agoraphobic​ (i.e., afraid to leave their​ homes). The following table indicates how many patients Dr. Fok has seen each year for the past 10 years. It also indicates what the robbery rate was in New Orleans during the same​ year.                                                                                                                                          

Year	1	2	3	4	5	6	7	8	9	10
Number of Patients	37	34	40	41	41	54	60	53	58	62
Robbery Rate per​ 1,000 Population	58.0	60.6	73.0	75.7	81.5	89.0	101.5	94.2	104.1	116.2

The simple linear regression equation that shows the best relationship between the number of patients and year is ​(round your responses to three decimal​ places):

                                               

ModifyingAbove y with carety ​=??????​+??????x where

ModifyingAbove y with carety ​= Dependent Variable and x​ = Independent Variable.

Using linear regression​, the number of patients Dr. Fok will see in year 11​=????? patients​ (round your response to two decimal​ places).

Using linear regression​, the number of patients Dr. Fok will see in year 12​=???? patients ​(round your response to two decimal​ places).

The coefficient of determination for the linear regression model is 0.8621 This shows that there is a (strong) OR (not so strong) relationship between the​ "Number of​ Patients" and​ "Year."

Answer 1

Year	Number of Patients	Robbery rate per 1,000 Population
1	37	58
2	34	60.6
3	40	73
4	41	75.7
5	41	81.5
6	54	89
7	60	101.5
8	53	94.2
9	58	104.1
10	62	116.2

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.928462
R Square	0.862041
Adjusted R Square	0.844796
Standard Error	4.110961
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	844.8	844.8	49.98817	0.000105
Residual	8	135.2	16.9
Total	9	980
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	30.4	2.808321	10.82497	4.68E-06	23.924	36.876	23.924	36.876
Year	3.2	0.452602	7.070231	0.000105	2.156298	4.243702	2.156298	4.243702

So, the simple linear equation is,

Number of Patients = 30.400 + 3.2 * Year

the number of patients Dr. Fok will see in year 11​= 30.4 + 3.2 * 11

= 65.60 Patients.

the number of patients Dr. Fok will see in year 12​ = 30.4 + 3.2 * 12

= 68.80 Patients.

and,

The coefficient of determination for the linear regression model is 0.8621. This shows that there is a strong relationship between the​ "Number of​ Patients" and​ "Year."