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	35	32	41	41	42	54	62	53	58	62
Robbery Rate per​1,000 Population	58.3	60.6	73.0	75.7	81.5	89.5	99.6	94.8	103.2	115.6

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 ​=?+?x

where

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

Answer 1

Year(X) No of patients(Y) XY X^2 (square of X)

1 35 35 1

2 32 64 4

3 41 123 9

4 41 164 16

5 42 210 25

6 54 330 36

7 62 434 49

8 53 424 64

9 58 522 81

10 62 620 100

X = 1+2+3+4+5+6+7+8+9+10 = 55

Y = 35+32+41+41+42+54+62+53+58+62 = 480

XY = 35+64+123+168+205+330+406+424+522+620 = 2897

X^2 = 1+4+9+16+25+36+49+64+81+100 = 385

Number of periods = n = 10

X-bar = X/n = 55/10 = 5.5

Y-bar = Y/n = 480/10 = 48.0

b = [ XY - (n. X-bar. Y-bar)] / [ X^2 - (n. Square of X-bar)]

= [2897 - (10 x 5.5 x 48.0)] / [385 - (10 x 5.5 x 5.5)]

= (2897 - 2640)/(385-302.5)

= 257/82.5

= 3.115

a = Y-bar - (b. X-bar) = 48.0 - (3.115 x 5.5) = 48.0-17.1325 = 30.868

So the regression equation is Y = a+bx => Y = 30.868+3.115x