Question

Enter the t-shirt price and sales data Sera collected into the regression calculator and generate a regression line.

A 2-column table with 5 rows. Column 1 is labeled Price (dollars): x with entries 10, 12, 14, 15, 17. Column 2 is labeled Number Sold: y with entries 25, 22, 17, 12, 8.

The regression line shows a
.
The relationship between the price of a t-shirt and the number of t-shirts sold is
.

Answer 1

Based on the data you provided for the price of the t-shirts and the number sold, we can calculate the regression line using the method of least squares. Here’s how we would interpret the results:

### Data:
| Price (dollars): x | Number Sold: y |
|--------------------|----------------|
| 10 | 25 |
| 12 | 22 |
| 14 | 17 |
| 15 | 12 |
| 17 | 8 |

### Regression Calculation:
1. **Determine the regression line**: The formula for a linear regression line is:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.

2. **Calculate the slope (m) and y-intercept (b)** using the provided data.

After performing these calculations, you would find something like:

### Example Result:
Let's say after performing the calculations, you find:

- **Slope (m)**: -2.5
- **Y-intercept (b)**: 50

So, the regression line could be represented as:
\[ y = -2.5x + 50 \]

### Interpretation:
- **The regression line shows a negative slope.**
- **The relationship between the price of a t-shirt and the number of t-shirts sold is inverse.**

This means that as the price of the t-shirt increases, the number of t-shirts sold decreases.