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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
.

1 answer

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.