Scatter Plot Math Example 4
Follow the full solution, then compare it with the other examples linked below.
Example 4
hardA scatter plot of age vs. reaction time shows a curved upward pattern (reaction time increases with age, faster for older individuals). Why would fitting a straight line to this data be problematic?
Solution
- 1 The relationship is non-linear (curved), so a straight line would systematically underestimate reaction time for young and old individuals and overestimate for middle-aged
- 2 Residuals would show a clear pattern (not random), violating the linearity condition for regression
- 3 A linear model would have poor fit (low ) and misleading predictions outside observed range
Answer
A straight line is inappropriate for curved data; it produces systematic errors in prediction and violates regression assumptions.
The form of a scatter plot determines which model is appropriate. A curved pattern requires non-linear models (quadratic, exponential, etc.). Forcing a linear fit creates biased predictions and untrustworthy inference.
About Scatter Plot
A scatter plot is a graph with one quantitative variable on each axis where each data point is plotted as a dot, revealing relationships between the two variables.
Learn more about Scatter Plot →More Scatter Plot Examples
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