Question

10. Answer True or False for the following statements. If false, justify what would make the statement true. a. If the least-squares equation relating the independent variable x and the dependent variable y for a given problem is y = 2x + 5, then an increase of 1 unit in x is associated with an increase of 2 units in y. b. If your computed correlation coefficient is r = +1.2, then you have better than a perfect positive correlation. c. A student might expect that there is a positive correlation between the age of his or her laptop and its resale value. d. In simple regression analysis, if the slope of the line is positive, then there is a positive correlation between the dependent variable y and the independent variable x. e. If there is no correlation between the independent and dependent variables, then the value of the correlation coefficient must be –1.

Answer 1

a) TRUE

b) FALSE

c) FALSE

d) TRUE

e) FALSE

Explanation:

a)

TRUE because the slope of the correlation line is 2 and this is the rate of change of y respect to x

b)

FALSE

The correlation coefficient r is always between -1 and 1, so it can never be greater than one

c)

FALSE

A student might expect that there is a positive correlation between the age of their laptop and its resale value only if after collecting a large enough sample of data that relates age of the student and price of resale of their laptop, he or she finds that there is a positive correlation coefficient r>0

d)

TRUE

If there is a positive correlation, then the greater the x, the greater the y

e)

FALSE

If there is no correlation between the independent and dependent variables, then the value of the correlation coefficient must be 0.