Multiple Choice
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?
12. Regression
Quadratic Regression
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For the data points in the graphs below, which most likely suggests a quadratic relationship?
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B
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D
Verified step by step guidance1
Step 1: Understand the types of relationships shown in scatter plots. A linear relationship shows points roughly along a straight line, either increasing or decreasing. A quadratic relationship typically shows a curved pattern, often resembling a parabola (U-shaped or inverted U-shaped).
Step 2: Examine the first scatter plot. The points appear scattered without any clear pattern, so this does not suggest a quadratic relationship.
Step 3: Examine the second scatter plot. The points form a curve that starts low and rises sharply, resembling an exponential or quadratic growth pattern. This could suggest a quadratic relationship.
Step 4: Examine the third scatter plot. The points form a clear U-shaped curve, which is characteristic of a quadratic relationship where the dependent variable decreases and then increases as the independent variable changes.
Step 5: Examine the fourth scatter plot. The points form a straight line with a downward trend, indicating a linear negative relationship, not quadratic.
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