Question

omework: Ch 04 HW 2 ore: 0 of 20 pts roblem 4.39 Or. Lillian Fok, 4 of 6 (4 complete) ▼ HW Score: 30%, 3 Question l how many patients a New Orleans psychologist, specializes in treating patients who are agoraphobic (i.e, afraid to leave their homes). The following table indicates has seen each year for the past 10 years. It also indicates what the robbery rate was in New Orleans during the s ame year Year Number of Patients 35 32 40 40 41 62 54 59 Robbery Rate pe 58.3 61.4 73.075.7 81.1 89.0101.1 94.8 102.2 115.6 1,000 Population 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 where y- Dependent Variable and x Independent Variable Enter your answer in the edit fields and then click Check Answer Clear Al 3 pemaining

Answer 1

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

1 35 35 1

2 32 64 4

3 40 120 9

4 40 160 16

5 41 205 25

6 55 330 36

7 62 434 49

8 54 432 64

9 59 531 81

10 60 600 100

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

$\sum$Y = 35+32+40+40+41+55+62+54+59+60 = 478

$\sum$XY = 35+64+120+160+205+330+434+432+531+600 = 2911

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

Number of periods = n = 10

X-bar = $\sum$X/n = 55/10 = 5.5

Y-bar = $\sum$Y/n = 478/10 = 47.8

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

= [2911 - (10 x 5.5 x 47.8)] / [385 - (10 x 5.5 x 5.5)]

= (2911 - 2629)/(385-302.5)

= 282/82.5

= 3.418

a = Y-bar - (b. X-bar) = 47.8 - (3.418 x 5.5) = 47.8-18.799 = 29.001

So the regression equation is Y = a+bx => Y = 29.001+3.418x