Multiple Choice
For the data points in the graphs below, which most likely suggests a quadratic relationship?
12. Regression
Quadratic Regression
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The data below shows the population of a small town (in 1000s) over a 9 year period. Using a graphing calculator, determine the linear & quadratic regression curves. Compare their values. Which model is a better fit for the data?
A
Both Linear with and quadratic with are good fits for the data.
B
Quadratic with is a better fit than linear with with .
C
Both Linear with and quadratic with are good fits for the data.
D
Quadratic with is a better fit than linear with with .
Verified step by step guidance1
Step 1: Enter the data into your graphing calculator by inputting the years as the independent variable (X) and the population values (in 1000s) as the dependent variable (Y).
Step 2: Use the calculator's regression function to calculate the linear regression model. This will provide you with the linear equation of the form $Y = a + bX$ and the coefficient of determination $R^2$ for the linear fit.
Step 3: Next, use the calculator to compute the quadratic regression model. This will give you a quadratic equation of the form $Y = a + bX + cX^2$ along with its $R^2$ value.
Step 4: Compare the $R^2$ values from both models. The $R^2$ value indicates how well the model fits the data, with values closer to 1 representing a better fit.
Step 5: Determine which model is better by selecting the one with the higher $R^2$ value. In this case, the quadratic model typically has a higher $R^2$, indicating it fits the population data better than the linear model.
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