Lecture 5

Question 1

The parameter ρ, the correlation coefficient satisfies

Answer 1

E[(x-μx)(y-μy)] = ρσxσy

Question 2

If the correlation coefficient = 0 then

Answer 2

x and y are independent

Question 3

The covariance of x and y is defined by

Answer 3

E[(x-μx)(y-μy)]

Question 4

If ρ > 0 then

Answer 4

positive correlation y tends to increase as x increases

Question 5

If ρ < 0 then

Answer 5

negative correlation y tends to decrease as x increases

Question 6

Pearson’s product moment correlation coefficient

Answer 6

r = 1/n-1 (xi-x̄/sx)(xi-ȳ/sy)

where x̄ is the sample mean
and sx the sample standard deviation

Question 7

Ordinary least squares fitting

Answer 7

yi = a + bxi + ε

Question 8

correlation coefficient is independent of

Answer 8

scaling