Christine is interested in buying a new backpack. She compares the price and volume of several backpacks. Christine finds that the relationship between price and volume can be described by the following least square regression line:

Question

Predicted Price = 890 - 105(Backpack Volume).
What is the slope of Christine's data?
A.
-105 price/volume
B. -105 volume/price
C.
105 price/volume
D. 105 volume/price

Answer 1

In the least squares regression line given by the equation:

\[ \text{Predicted Price} = 890 - 105(\text{Backpack Volume}), \]

the slope of the regression line is the coefficient of the independent variable, which in this case is the Backpack Volume.

The slope is \(-105\). This means that for every unit increase in the Backpack Volume, the predicted price decreases by 105 units of currency.

The correct interpretation of the slope is as follows:

• It indicates how much the price changes with respect to a unit change in volume.

The units of the slope (in this context) indicate a change in price for every unit of volume. Thus, the correct answer is:

A. -105 price/volume.