Question

Scores on the 1995 SAT verbal aptitude test x among Kentucky high school seniors were normally distributed with mean 420 and standard deviation 80. Scores on the 1995 SAT quantitative aptitude test y among Kentucky high school seniors were normally distributed with mean 440 and standard deviation 60. The least-squares regression line has the equation y = .6x + 188. The correlation between verbal scores and math scores is:________.
a) –.8
b) 0
c) .45
d) .8
e) cannot be determined from the information given

Answer 1

Answer:

d. 0.80

Step-by-step explanation:

The given regression equation is

y=0.6x+188

Here, slope=b=0.6

xbar=420, sx=80, ybar=440 and sy=60.

As we know that when y=a+bx, the slope is

b=r(sy/sx)

From this equation we can find correlation coefficient r

b*sx=r*sy

bsx/sy=r

r=0.6*80/60=48/60=0.80.

Hence the correlation coefficient r=0.8.