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. $$\begin{array} { | l | l | l | }
\hline & \text { PRICE PER POUND } & \text { POUNDS SOLD } \
\hline & \$ 3.99 & 75 \
\hline & \$ 5.99 & 60 \
\hline & \$ 7.00 & 65 \
\hline & \$ 12.00 & 45 \
\hline & \$ 4.50 & 80 \
\hline & \$ 7.50 & 70 \
\hline & \$ 15.00 & 25 \
\hline & \$ 10.00 & 35 \
\hline & \$ 12.50 & 40 \
\hline & \$ 8.99 & 50 \
\hline \text { Mean } & & \
\hline \text { Correlation } & \$ 8.75 & 54.50 \
\hline
\end{array}$$ 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
A) 95.459.
B) .858.
C) -4.684.
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. $$\begin{array} { | l | l | l | } 
\hline & \text { PRICE PER POUND } & \text { POUNDS SOLD } \
\hline & \$ 3.99 & 75 \
\hline & \$ 5.99 & 60 \
\hline & \$ 7.00 & 65 \
\hline & \$ 12.00 & 45 \
\hline & \$ 4.50 & 80 \
\hline & \$ 7.50 & 70 \
\hline & \$ 15.00 & 25 \
\hline & \$ 10.00 & 35 \
\hline & \$ 12.50 & 40 \
\hline & \$ 8.99 & 50 \
\hline \text { Mean } & & \
\hline \text { Correlation } & \$ 8.75 & 54.50 \
\hline
\end{array}$$ 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
A) 95.459.
B) .858.
C) -4.684.
D) -.858.
E) -8.999.

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 $b_0 = \bar{y} - b_1\bar{x}$, where $\bar{y}$ is the mean of the response variable (pounds sold), $\bar{x}$ is the mean of the predictor variable (price per pound), and $b_1$ is the slope of the line. Given the correlation and means provided, and knowing that the slope $b_1$ is derived from the correlation coefficient, standard deviations, and means, the correct calculation would lead to an intercept that best supports the relationship between price and pounds sold as described. Option A, 95.459, is the correct choice because it represents a plausible intercept value for the regression line, given the context of the data. The other options do not align with the typical output of regression analysis in this context.

A Small Independent Organic Food Store Offers a Variety of Specialty