Question

11 advertising the table shows the number of items a business sells given the amount that they spend on advertising. the equation of the line of best fit for the data is y = 0.076x + 116.97.

a. interpret the slope and y - intercept of the regression equation in the context of the data.
the slope means that the number of items sold
by about
items for each dollar spent on advertising
the y - intercept means that when the business spent
on advertising, they sold about
items.

b. estimate the number of items the business will sell if they spend $3000 on advertising. write to the nearest whole number.
items

Explanation:

Step1: Analyze the slope

The equation of the line of best fit is \(y = 0.076x+116.97\). In the linear equation \(y = mx + b\) (where \(m\) is the slope and \(b\) is the \(y\) - intercept), for each increase of \(x\) (advertising spend) by \(1\) dollar, \(y\) (number of items sold) changes by \(m\). Since \(m = 0.076\approx0.08\), the number of items sold increases by about \(0.08\) items for each dollar spent on advertising.

Step2: Analyze the \(y\) - intercept

When \(x = 0\) (the business spent \(\$0\) on advertising), \(y=b\). Substituting \(x = 0\) into \(y=0.076x + 116.97\), we get \(y=116.97\approx117\). So when the business spent \(\$0\) on advertising, they sold about \(117\) items.

Step3: Estimate the number of items for \(x = 3000\)

Substitute \(x = 3000\) into the equation \(y=0.076x+116.97\).

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Answer:

A. The slope means that the number of items sold increases by about \(0.08\) items for each dollar spent on advertising. The \(y\) - intercept means that when the business spent \(\$0\) on advertising, they sold about \(117\) items.
B. \(345\) items.