A small independent organic food store offers a variety of specialty coffees.To determine whether price has an impact on sales, the managers kept track of how many pounds of each
Variety of coffee were sold last month. $$\begin{array} { | l | l | l | }
\hline & \text { PRICE PER POUND } & \text { POUNDS SOLD } \
\hline & \$ 3.99 & 75 \
\hline & \$ 5.99 & 60 \
\hline & \$ 7.00 & 65 \
\hline & \$ 12.00 & 45 \
\hline & \$ 4.50 & 80 \
\hline & \$ 7.50 & 70 \
\hline & \$ 15.00 & 25 \
\hline & \$ 10.00 & 35 \
\hline & \$ 12.50 & 40 \
\hline & \$ 8.99 & 50 \
\hline \text { Mean } & & \
\hline \text { Ctandard } & \$ 8.75 & 54.50 \
\hline \text { Deviation } & & 18.33 \
\hline
\end{array}$$ Based on the data and summary statistics, the intercept of the estimated regression line that
Relates the response variable (monthly sales) to the predictor variable (price per pound) is

Question

A small independent organic food store offers a variety of specialty coffees.To determine whether price has an impact on sales, the managers kept track of how many pounds of each
Variety of coffee were sold last month. $$\begin{array} { | l | l | l | } 
\hline & \text { PRICE PER POUND } & \text { POUNDS SOLD } \
\hline & \$ 3.99 & 75 \
\hline & \$ 5.99 & 60 \
\hline & \$ 7.00 & 65 \
\hline & \$ 12.00 & 45 \
\hline & \$ 4.50 & 80 \
\hline & \$ 7.50 & 70 \
\hline & \$ 15.00 & 25 \
\hline & \$ 10.00 & 35 \
\hline & \$ 12.50 & 40 \
\hline & \$ 8.99 & 50 \
\hline \text { Mean } & & \
\hline \text { Ctandard } & \$ 8.75 & 54.50 \
\hline \text { Deviation } & & 18.33 \
\hline
\end{array}$$ Based on the data and summary statistics, the intercept of the estimated regression line that
Relates the response variable (monthly sales) to the predictor variable (price per pound) is

Quizplus · Accepted Answer

The intercept of the estimated regression line can be calculated using the formula for the intercept in a simple linear regression, which is $\bar{y} - b\bar{x}$, where $\bar{y}$ is the mean of the dependent variable (pounds sold), $\bar{x}$ is the mean of the independent variable (price per pound), and $b$ is the slope of the line. Given the mean price per pound is \$8.75 and the mean pounds sold is 54.5, and without the slope directly provided but knowing the relationship between price and quantity sold is generally negative (as price increases, quantity sold decreases), the only positive intercept option provided that makes sense with the given means is 95.459. This suggests that if the price were \$0, the model predicts sales of 95.459 pounds, assuming the linear relationship holds.

A Small Independent Organic Food Store Offers a Variety of Specialty