Question

You are given a various set of values: xbar = 12 ybar = 16 r = .46 Sy = 18 Sx = 6 Find a and b, then write them as an equation for a line. b = a = yhat =

Answer 1

Slope, b = 1.38 ; intercept, a = - 0.56 ;

Y = - 0.56 + 1.38x

Explanation:

Given that :

xbar = 12

ybar = 16

r = .46

Sy = 18

Sx = 6

The equation of a line can be expressed as :

Y = a + bx

Where ;

a = intercept ; b = slope ; x = independent variable ; y = dependent variable

The slope b ; can be obtained using the relation :

b = r(Sy / Sx)

= 0.46(18/6)

= 0.46(3)

= 1.38

The intercept a, can be obtained using the relation :

Ybar - b(Xbar)

16 - 1.38(12)

16 - 16.56

a = - 0.56

Hence ;

Slope, b = 1.38 ; intercept, a = - 0.56

Th equation of the line will be :

Y = - 0.56 + 1.38x