Question

Use quadratic regression to write a function for the data in the table.

A) Determine the correlation coefficient for the data.
B) Find the quadratic equation that models the relationship.
C) Calculate the mean of the data points.
D) Identify the outlier in the dataset.

Answer 1

In quadratic regression, you first determine the independent and dependent variables, create a scatter plot, calculate the regression equation, and find the correlation coefficient. You then calculate the mean of the data points and identify any outliers.

Step-by-step explanation:

To use quadratic regression to write a function for a given dataset, you would generally follow these steps:

1. Determine the independent and dependent variables for a scatter plot.
2. Using a statistical calculator or software, enter the data and create the scatter plot.
3. Calculate the quadratic regression equation using the regression function on the calculator or software. This will typically be in the form ý = ax² + bx + c.
4. Find the correlation coefficient (R-squared value) to determine how well the equation models the data. A correlation coefficient close to 1 indicates a strong positive relationship.
5. Calculate the mean (average) of the data points by adding all the data values together and dividing by the number of data points.
6. Identify the outlier by looking for a data point that is significantly distant from the trend of the rest of the data.

For more specific tasks like finding the mean CPI for a particular year or estimating values based on the regression line, you would use the regression equation and possibly other statistical formulas or software features.