The New York Times study of homes reported average house size in 2001 to be 2,428 square feet, compared with an average of 2,150 square feet in 1987. Suppose a study of homes over the years recorded the year from 1987 to the present, as well as the size of the house in square feet, to see if average house size increased steadily over time. Tell whether the variables are categorical or quantitative. Also, tell which is the role of explanatory variable and which is the response variable.
In this scenario, we have two variables: "year" and "house size in square feet."
The variable "year" represents a categorical variable since it represents different time periods (1987, 2001, etc.).
On the other hand, the variable "house size in square feet" represents a quantitative variable since it represents the numerical measurement of the size of the houses.
Now, let's determine which variable is the explanatory variable (independent variable) and which one is the response variable (dependent variable).
The explanatory variable is the variable that is hypothesized to cause a change or have an impact on the response variable. In this case, the variable "year" could be considered as the explanatory variable because it represents the different time periods. By analyzing the relationship between the year and the house size in square feet, we can examine if the average house size has changed over time.
The response variable is the variable that is expected to change as a result of the explanatory variable. In this case, the response variable would be "house size in square feet" because it is the variable that is expected to change depending on the time period.
To summarize:
- Categorical variable: Year
- Quantitative variable: House size in square feet
- Explanatory variable: Year
- Response variable: House size in square feet
The variables in this case are both quantitative. The year from 1987 to the present is a numerical variable, and the size of the house in square feet is also a numerical variable.
The explanatory variable, in this case, would be the year from 1987 to the present. It is the variable that is believed to have an effect on the response variable.
The response variable is the size of the house in square feet. It is the variable that is believed to be influenced by the explanatory variable.