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?

Answer 1

Answer:

c) $y=16.57+1.83x$

Step-by-step 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

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

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)

$m=r\frac{S_{y}}{S_{x}}\\\\m=(0.88)\frac{27}{13}\\\\m=1.83$

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

Putting these values of m and b in (1)

$y=1.83x+16.57$