Chapter 29, Problem 1E

a.

To determine

Suggest the specific indicator that should be used in a regression to predict income for the sex of respondents, in a survey.

Answer to Problem 1E

The specific indicators that should be used in a regression to predict income for the sex of respondents, in a survey is:

$sex=\{\begin{array}{l}1,\text{ if the respondent is female}\\ 0,\text{ if the responsent is male}\text{.}\end{array}$

Or, $sex=\{\begin{array}{l}1,\text{ if the respondent is male}\\ 0,\text{ if the responsent is female}\text{.}\end{array}$

Explanation of Solution

Justification:

Indicator variable:

An indicator variable is a variable assigned to a qualitative predictor variable that has more than one categories, which takes values 1 or 0. The value 1 denotes the presence of the particular category for which the indicator variable is created and the value 0 denotes the absence of that category.

The sex of individuals does not take any natural numerical value. Thus, the value 1 may be assigned to either males or females, as per the choice of the researcher.

Thus, the specific indicators that should be used in a regression to predict income for the sex of respondents, in a survey is:

$sex=\{\begin{array}{l}1,\text{ if the respondent is female}\\ 0,\text{ if the responsent is male}\text{.}\end{array}$

Or, $sex=\{\begin{array}{l}1,\text{ if the respondent is male}\\ 0,\text{ if the responsent is female}\text{.}\end{array}$

b.

To determine

Suggest the specific indicator that should be used in a regression to predict the square footage available for rent in a commercial building, for denoting the number of stories in the building.

Answer to Problem 1E

The number of stories in a commercial building is better to be treated as a quantitative variable.

Explanation of Solution

Justification:

The study does not categorize the number of floors, such as ‘greater than 5 floors’ and ‘less than 5 floors’. Rather, it considers the actual number of floors in the building to create the regression model. In such a case, the number of floors can take several numerical values.

Thus, the number of stories in a commercial building is better to be treated as a quantitative variable.

c.

To determine

Suggest the specific indicator that should be used in a regression to predict the amount an individual’s medical insurance would pay for an operation, to check whether an individual was over 65 and eligible for Medicare.

Answer to Problem 1E

The specific indicator that should be used in a regression to predict the amount an individual’s medical insurance would pay for an operation, to check whether an individual was over 65 and eligible for Medicare is:

$age=\{\begin{array}{l}1,\text{ if the individual is above 65}\\ 0,\text{ if the individual is below 65}\text{.}\end{array}$

Or, $age=\{\begin{array}{l}1,\text{ if the individual is below 65}\\ 0,\text{ if the individual is above 65}\text{.}\end{array}$

Explanation of Solution

Justification:

The category whether an individual is above or below 65 does not take any natural numerical value. Thus, the value 1 may be assigned to either of the groups, as per the choice of the researcher.

Thus, the specific indicator that should be used in a regression to predict the amount an individual’s medical insurance would pay for an operation, to check whether an individual was over 65 and eligible for Medicare is:

$age=\{\begin{array}{l}1,\text{ if the individual is above 65}\\ 0,\text{ if the individual is below 65}\text{.}\end{array}$

Or, $age=\{\begin{array}{l}1,\text{ if the individual is below 65}\\ 0,\text{ if the individual is above 65}\text{.}\end{array}$