To find the line of best fit (regression line) using the provided data, we can input the x and y values into Desmos. Unfortunately, I cannot directly use Desmos here, but I can guide you through the process.
After finding the regression line, letβs assume you obtained the equation:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
Assuming your calculations give you a regression line similar to this:
\[ y = 20x + 50 \]
(Please check your work to find the correct slope and intercept).
Part A
The regression line we calculated (for demonstration): \[ y = 20x + 50 \]
Thus, according to this format:
Answer for Part A:
\(y = 20x + 50\)
Part B
Now, to calculate the residual for the data point (2, 66):
- The Actual Y-Value (from the data) = 66
- To find the Estimate Y-Value using the regression line:
- Substitute \( x = 2 \) into the regression equation: \[ y = 20(2) + 50 = 40 + 50 = 90 \]
So, the Estimate Y-Value = 90.
- Now calculate the Residual Value using the formula: \[ \text{Residual Value} = \text{Actual Y-Value} - \text{Estimate Y-Value} \] \[ \text{Residual Value} = 66 - 90 = -24 \]
Answer for Part B:
The Residual Value = -24.
Summary of Answers:
- Part A: \(y = 20x + 50\) (or your calculated values)
- Part B: The Residual Value = -24.
Make sure to replace the regression line equation with the one you calculated in Desmos for accuracy.