To analyze what the slope of the model represents, let's follow a logical sequence of reasoning based on the given data.
1. We are provided with the data that shows the number of cereal boxes sold on different days.
2. The days are recorded as: 5, 3, 8, 6, 0, and 4.
3. The corresponding number of cereal boxes sold on those days are: 50, 70, 20, 40, 100, and 60.
By fitting a linear regression model to this data, we can determine the relationship between the number of days and the number of cereal boxes sold. The slope of the linear regression line provides information about the rate of change between these two variables.
- Slope Interpretation:
- The slope of a linear regression line (often denoted as [tex]\( m \)[/tex] in the equation [tex]\( y = mx + c \)[/tex]) indicates how much the dependent variable [tex]\( y \)[/tex] changes for a one-unit change in the independent variable [tex]\( x \)[/tex].
- In this context, [tex]\( x \)[/tex] is the number of days and [tex]\( y \)[/tex] is the number of cereal boxes sold.
- Therefore, the slope in this model represents the change in the number of cereal boxes sold per day.
Given the slope calculated from the data is [tex]\(-10.000000000000004\)[/tex], which is a negative value, it indicates that for every additional day, the store sells 10 fewer cereal boxes on average.
So, the correct choice for what the slope of the model represents is:
- The number of cereal boxes sold per day
