Question

monthly sales & advertising costs
the slope of the trend line is 15. what does that mean
in regard to the data of the scatterplot? check all that
apply.
the slope represents the rate of change of the data.
advertising costs increase $15,000 as sales
increase by $1,000.
sales increase $15,000 as ads increase by $1,000.
a positive slope infers a negative correlation.
a positive slope infers a positive correlation.

Explanation:

• The slope in a linear relationship represents the rate of change. In a scatter - plot with a trend line, it shows how one variable changes with respect to the other.
• For the variables here (sales \(y\) and advertising costs \(x\), both in units of \(\$1000\)), the formula for the slope of a line \(y = mx + b\) is \(m=\frac{\Delta y}{\Delta x}\). A slope \(m = 15\) means that for a unit change in \(x\) (advertising costs, \(\Delta x=1\) which is \(\$1000\) increase in advertising costs), there is a change in \(y\) (sales) of \(\Delta y = 15\) (which is \(\$15000\) increase in sales).
• A positive slope indicates a positive correlation, meaning as one variable (advertising costs) increases, the other variable (sales) also increases.

Answer:

• The slope represents the rate of change of the data.
• Sales increase \(\$15,000\) as ads increase by \(\$1,000\).
• A positive slope infers a positive correlation.