Question

We know that a researcher calculated a correlation coefficient for the association between smoking and lung cancer rate is 0.737 using the data in Table 1. In addition, the researcher have estimated x ̅ = 603.64, y ̅ = 20.55, s_x= 378.451, s_y= 11.725, and r = 0.737.

a. Calculate the slope coefficient b for y ̂ = a + bx. Round the answer to the nearest 10,000th

b=

b. Calculate the intercept coefficient a for y ̂ = a + bx. Round the answer to the nearest 100th.

a=

c. What is the estimated linear regression equation?

y ̂ =

d. What is the predicted lung cancer rate in a country with a per capita cigarette consumption of 400? Round the answer to the nearest 100th.

Answer 1

a) Given  S_{​​​​​​x}​​​​​ = 378.451 Sy= 11.725 , r = 0.737

Slope. b = r * (S_{​​​​​​y} /S_{​​​​​​x}​​​ ) = 0.737*(11.725/378.451)

b = 0.0228

b) Given. X^{​​​​​​} bar = 603.64 and y bar = 20.55

Intercept a = ybar - (b* x bar )

a = 20.55 - (0.0228*603.64)

a = 6.79

c) the estimated regression equation is

y^{​​​​​​^} = 6.79 + 0.0228 * x

d) here we asked the predicted lung cancer rate ( y^{​​​​​​^} ) for per capita cigarette consumption x = 400

y^{​​​​​​^} = 6.79 + 0.0228*400

y^{​​​​​​^} = 15.91