Answer :
### 1. Which drink did you select? Circle one.
[tex]\[ \text{Coffee} \][/tex]
### 2. Find a line of best fit.
To find the line of best fit (linear regression) for the coffee sales data, we will identify the slope [tex]\(a\)[/tex] and the y-intercept [tex]\(b\)[/tex] of the line that best fits the data points.
Given the following data for coffee sales:
Price (in dollars) and Sales (number of cups):
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline \text{Price:} & 1.50 & 2.20 & 2.70 & 2.50 & 2.90 & 2.00 & 1.60 & 2.10 & 3.00 & 1.80 \\ \hline \text{Sales:} & 96 & 79 & 70 & 73 & 64 & 85 & 94 & 83 & 63 & 91 \\ \hline \end{array} \][/tex]
Using linear regression, we determine the equation of the line of best fit, which can be written in the form:
[tex]\[ y = ax + b \][/tex]
Where:
- [tex]\( y \)[/tex] is the number of cups sold (Sales)
- [tex]\( x \)[/tex] is the price (Price)
- [tex]\( a \)[/tex] is the slope of the line
- [tex]\( b \)[/tex] is the y-intercept
After performing the linear regression calculation:
### Results:
- The slope [tex]\(a\)[/tex] (rounded to the nearest tenth): [tex]\[-22.7\][/tex]
- The y-intercept [tex]\(b\)[/tex] (rounded to the nearest tenth): [tex]\[130.3\][/tex]
Therefore, the line of best fit for the coffee sales data is given by the equation:
[tex]\[ y = -22.7x + 130.3 \][/tex]
This equation indicates that for each dollar increase in the price of coffee, the sales decrease by approximately 22.7 cups per day, starting from an initial value of approximately 130.3 cups sold when the price is $0.
[tex]\[ \text{Coffee} \][/tex]
### 2. Find a line of best fit.
To find the line of best fit (linear regression) for the coffee sales data, we will identify the slope [tex]\(a\)[/tex] and the y-intercept [tex]\(b\)[/tex] of the line that best fits the data points.
Given the following data for coffee sales:
Price (in dollars) and Sales (number of cups):
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline \text{Price:} & 1.50 & 2.20 & 2.70 & 2.50 & 2.90 & 2.00 & 1.60 & 2.10 & 3.00 & 1.80 \\ \hline \text{Sales:} & 96 & 79 & 70 & 73 & 64 & 85 & 94 & 83 & 63 & 91 \\ \hline \end{array} \][/tex]
Using linear regression, we determine the equation of the line of best fit, which can be written in the form:
[tex]\[ y = ax + b \][/tex]
Where:
- [tex]\( y \)[/tex] is the number of cups sold (Sales)
- [tex]\( x \)[/tex] is the price (Price)
- [tex]\( a \)[/tex] is the slope of the line
- [tex]\( b \)[/tex] is the y-intercept
After performing the linear regression calculation:
### Results:
- The slope [tex]\(a\)[/tex] (rounded to the nearest tenth): [tex]\[-22.7\][/tex]
- The y-intercept [tex]\(b\)[/tex] (rounded to the nearest tenth): [tex]\[130.3\][/tex]
Therefore, the line of best fit for the coffee sales data is given by the equation:
[tex]\[ y = -22.7x + 130.3 \][/tex]
This equation indicates that for each dollar increase in the price of coffee, the sales decrease by approximately 22.7 cups per day, starting from an initial value of approximately 130.3 cups sold when the price is $0.
