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	3636	3434	4141	4040	4040	5656	5858	5353	5959	6262
Robbery Rate per​ 1,000 Population	58.058.0	60.660.6	73.473.4	75.275.2	81.581.5	89.589.5	101.1101.1	94.294.2	102.2102.2	116.2116.2

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):

                                               

^

Y= _____+_____x

^

where Y ​= 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).

Answer 1

Answer a) Formulate a Linear Equation using the following steps:

Step 1: Let x = Independent Variable = No. of particular year, and y = Dependent Variable = No. No. of patients. First, prepare the following table:

Step 2: Find the column of xy, , and . Further, Find their total values as mentioned below:

Where,

xy = x * y,

= x * x

= y * y

Hence, we get,

Step 3: Find the values of 'a' as mentioned below:

Hence, a =

=

=

= 3023.267 (Rounded to 3 decimal places)

Step 4: Find the values of 'b' as mentioned below:

Hence, b =

=

=

= 329.933 (Rounded to 3 Decimal Places)

Step 5: Determine the regression equation:

= a + b X

Where a = 3023.267 (As per step 3), and b= 329.933 (As per step 4)

Hence, = 3023.267 + 329.933 X

Answer b) Forecast the no. of patients when Year = X = 11

By replacing the value of x in regression equation derived in step 5 of answer a), we get

= 3023.267 + 329.933 (11)

= 3023.267 + 3629.263

= 6652.53 Patients (Rounded to 2 decimal places)

Answer c) Forecast the no. of patients when Year = X = 12

By replacing the value of x in regression equation derived in step 5 of answer a), we get

= 3023.267 + 329.933 (12)

= 3023.267 + 3959.196

= 6982.46 Patients (Rounded to 2 decimal places)