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. $$\begin{array} { | l | l | l | }
\hline & \text { PRICE PER POUND } & \text { POUNDS SOLD } \
\hline & \$ 3.99 & 75 \
\hline & \$ 5.99 & 60 \
\hline & \$ 7.00 & 65 \
\hline & \$ 12.00 & 45 \
\hline & \$ 4.50 & 80 \
\hline & \$ 7.50 & 70 \
\hline & \$ 15.00 & 25 \
\hline & \$ 10.00 & 35 \
\hline & \$ 12.50 & 40 \
\hline \text { Mean } & \$ 8.99 & 50 \
\hline \text { Standard } & & \
\hline \text { Deviation } & \$ 3.63 & 54.50 \
\hline & & 18.33 \
\hline
\end{array}$$ Based on the data and summary statistics shown below, the slope of the estimated regression
Line that relates the response variable (monthly sales) to the predictor variable (price per
Pound) is
A)95.459.
B).858.
C)-4.681.
D)-.858.
E)-8.999.

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. $$\begin{array} { | l | l | l | } 
\hline & \text { PRICE PER POUND } & \text { POUNDS SOLD } \
\hline & \$ 3.99 & 75 \
\hline & \$ 5.99 & 60 \
\hline & \$ 7.00 & 65 \
\hline & \$ 12.00 & 45 \
\hline & \$ 4.50 & 80 \
\hline & \$ 7.50 & 70 \
\hline & \$ 15.00 & 25 \
\hline & \$ 10.00 & 35 \
\hline & \$ 12.50 & 40 \
\hline \text { Mean } & \$ 8.99 & 50 \
\hline \text { Standard } & & \
\hline \text { Deviation } & \$ 3.63 & 54.50 \
\hline & & 18.33 \
\hline
\end{array}$$ Based on the data and summary statistics shown below, the slope of the estimated regression
Line that relates the response variable (monthly sales) to the predictor variable (price per
Pound) is
A)95.459.
B).858.
C)-4.681.
D)-.858.
E)-8.999.

Quizplus · Accepted Answer

The slope of the estimated regression line in a simple linear regression can be calculated using the formula $slope = \frac{r \cdot s_y}{s_x}$, where $r$ is the correlation coefficient, $s_y$ is the standard deviation of the response variable (pounds sold), and $s_x$ is the standard deviation of the predictor variable (price per pound). Given the negative relationship observed in the data (as price increases, pounds sold tends to decrease), and the provided standard deviations, the correct slope must be negative, making -4.681 the plausible choice given the options and the context of the question.

A Small Independent Organic Food Store Offers a Variety of Specialty