Question

The correlation analysis assumes that the measurements have a bivariate normal distribution in the population. Select all of the features that define a bivariate normal distribution.

A. Bell-shaped probability distribution in two dimensions rather than one
B. A relationship between X and Y that is not linear
C. The presence of outliers
D. Either X or Y has a decidedly skewed distribution
E. A relationship between X and Y that is linear
F. A cloud of points that is funnel shaped (wider at one end than the other)
G. The frequency distributions of X andY separately are normal

Answer 1

A. True

B. True

C. False

D. False

E. False

F. False

G. True

Explanation:

Select all of the features that define a bivariate normal distribution.

(this means that we select only those that are properties of the bivariate normal distribution)

A. Bell-shaped probability distribution in two dimensions rather than one

TRUE because any combination of the two is still normal Z(x,y)=aX+bY

B. A relationship between X and Y that is not linear

TRUE The contours of the distribution are ellipses.

C. The presence of outliers

FALSE possible, but not always.

D. Either X or Y has a decidedly skewed distribution

FALSE normal distributions are symmetric

E. A relationship between X and Y that is linear

FALSE see answer to B

F. A cloud of points that is funnel shaped (wider at one end than the other)

FALSE normal distributions are symmetric

G. The frequency distributions of X andY separately are normal

TRUE For example, in Z(x,y)=aX+bY, putting a or b=0 means that X and Y separately are normal.