Chapter 7, Problem 27E

(a)

To determine

To explain whether or not each of these possible conclusions is justified.

Answer to Problem 27E

Not justified.

Explanation of Solution

The correlation between Age and Income as measured on $100$ people is $r=0.75$ . From this the conclusion is given as:

When age increases, income increases as well.

This conclusion is not justified because we do not know this from the correlation alone. That there may be non-linear relationship or outliers. As it does not necessarily means that as age increase so the income increases as well because it can decline to or it may remain constant.

(b)

To determine

To explain whether or not each of these possible conclusions is justified.

Answer to Problem 27E

Not justified.

Explanation of Solution

The correlation between Age and Income as measured on $100$ people is $r=0.75$ . From this the conclusion is given as:

The form of relationship between age and income is straight.

This conclusion is not justified because we cannot tell from the correlation on what form of the relationship it is that of age and income that is given in the question.

(c)

To determine

To explain whether or not each of these possible conclusions is justified.

Answer to Problem 27E

Not justified.

Explanation of Solution

The correlation between Age and Income as measured on $100$ people is $r=0.75$ . From this the conclusion is given as:

There are no outliers in the scatterplot of income versus age.

This conclusion is not justified because we do not know from the correlation coefficient that the scatterplot of income versus age will be containing outliers or not. It can be studied only through the graph of the scatterplot of income versus age.

(d)

To determine

To explain whether or not each of these possible conclusions is justified.

Answer to Problem 27E

Justified.

Explanation of Solution

The correlation between Age and Income as measured on $100$ people is $r=0.75$ . From this the conclusion is given as:

Whether we measure the age in years or months, the correlation will still be $0.75$ only.

This conclusion is justified because the correlation does not depend on the units used to measure the variables. Thus, correlation is not considered in units. So, age units in months or years will not affect the correlation calculated.