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A data set collects several characteristic variables of 20 residential properties in a midwestern city. The variables include the sale price, the finished area, the number of bedrooms, the number of bathrooms, and others. We want to use the finished area (in thousand square feet) to predict the sale price (in thousand dollars) using a linear regression model. The fitted least-squares regression line is \[ y = -131 + 186x \].

1. In this model, the response variable is ____________.
2. The explanatory variable is ____________.

Which one of the following statements is TRUE for interpreting the value of the slope?

A. The sale price of a property is expected to increase by $186,000 when the finished area decreases by 1000 square feet.
B. The sale price of a property is expected to increase by $186 when the finished area increases by 1000 square feet.
C. The sale price of a property is expected to increase by $186,000 when the finished area increases by 1000 square feet.
D. The sale price of a property is expected to increase by $186,000 when the finished area increases by 1 square foot.

Answer :

In a linear regression model, the slope represents the effect the explanatory variable has on the response variable. As per the given model and the value of the slope, for every increase of 1000 square feet in the finished area, the sale price of the property is expected to increase by 186,000.

In your question, you are dealing with a linear regression model where you are trying to predict the sale price of a property (the response variable), based on the finished area (the explanatory variable).

The given regression line equation is y = -131 + 186 * 2.

In such equations, the slope represents the relationship between the response and explanatory variables.

In this case, the slope is 186, which implies that for every increase in the finished area by one unit (1000 square feet), the predicted sale price increases by 186 units (186,000) considering everything else constant.

Therefore, the correct interpretation is: 'the sale price of a property is expected to increase by 186,000 when the finished area increases by 1000 square feet.'

Learn more about the topic of Linear Regression here:

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