Question

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 1

c)
`y=16.57+1.83x`

Explanation:

Equation for regression line of y on x is given as

`\hat{y}=mx+b --- (1)`

where

`\hat{y}` = predicted value

m = slope of line

b = intercept

m and b are found as

`m=r(S_(y))/(S_(x))---(2)\\\\b=\bar{y}-m\bar{x}---(3)`

r = correlation coefficient = 0.88

Sx = standard deviation for independent variable x = 13

Sy = standard deviation for dependent variable y = 27

`\bar{x}` = mean value of independent variable x = 21

`\bar{x}` = mean value of dependent variable y = 55

Substituting these values in (2) and (3)

`m=r(S_(y))/(S_(x))\\\\m=(0.88)(27)/(13)\\\\m=1.83`

`b=\bar{y}-m\bar{x}\\\\b=55-(1.827)(21)\\\\b=16.57`

Putting these values of m and b in (1)

`y=1.83x+16.57`