A bivariate data set has x = 21, sx = 13, y = 55, sy = 27, and r = .88. What is the equation for the regression line of y on x?

a. y=46.81+.39x
b. y=93.43+1.83x
c. y=16.57+1.83x
d. y=22.31+.39x
e. y=19.44-1.83x

Answer :

Answer:

c) [tex]y=16.57+1.83x[/tex]

Step-by-step explanation:

Equation for regression line of y on x is given as

[tex]\hat{y}=mx+b --- (1)[/tex]

where

[tex]\hat{y}[/tex] = predicted value

m = slope of line

b = intercept

m and b are found as

[tex]m=r\frac{S_{y}}{S_{x}}---(2)\\\\b=\bar{y}-m\bar{x}---(3)[/tex]

r = correlation coefficient = 0.88

Sx = standard deviation for independent variable x = 13

Sy = standard deviation for dependent variable y = 27

[tex]\bar{x}[/tex] = mean value of independent variable x = 21

[tex]\bar{x}[/tex] = mean value of dependent variable y = 55

Substituting these values in (2) and (3)

[tex]m=r\frac{S_{y}}{S_{x}}\\\\m=(0.88)\frac{27}{13}\\\\m=1.83[/tex]

[tex]b=\bar{y}-m\bar{x}\\\\b=55-(1.827)(21)\\\\b=16.57[/tex]

Putting these values of m and b in (1)

[tex]y=1.83x+16.57[/tex]

Other Questions