What can we say about the relationship between the correlation r and the slope b of the least-squares line for the same set of data? a. Both r and b always have values between - 1 and 1. b. r is always larger than b. c. r and b have the same sign ( + or - ). d. the slope b is always equal to the square of the correlation r. e. b is always larger than r.

Question

Mathematics

Nathaniel Owen

9 June, 20:59

What can we say about the relationship between the correlation r and the slope b of the least-squares line for the same set of data? a. Both r and b always have values between - 1 and 1. b. r is always larger than b. c. r and b have the same sign ( + or - ). d. the slope b is always equal to the square of the correlation r. e. b is always larger than r.

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George · Answer 1

Step-by-step explanation:

We are to find the relationship between the correlation r and the slope b of the least-squares line for the same set of data

Whenever correlation is positive slope is positive and similarly when correlation is negative slope is negative.

correlation coefficient can take values only between - 1 and 1 but for slope no restriction because it is the rate of change of dependent variable for a unit change in independent variable.

Out of the options given a is wrong as b can take any value

The slope b is not the square of r because if b is square of r b is always positive but not so.

r need not be larger than b,

Option e is wrong because b can take any value.

Option c is the only right choice.

c. r and b have the same sign ( + or - )