Common Mistakes
Overview
Learn to recognize and avoid the most common errors students make when working with scatter plots, correlations, and lines of best fit. Understanding these mistakes will help you avoid them on tests and assignments.
Practice Problems
Question 1: A student sees a strong correlation between shoe size and vocabulary test scores in a school. They conclude bigger feet cause better vocabulary. What is the error?
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Answer: Confusing correlation with causation
Age is the lurking variable - older students have bigger feet AND larger vocabularies. Correlation does not prove one variable causes changes in another.
Question 2: A line of best fit has equation y = 3x + 10. A student calculates y when x = 5 as y = 3(5) = 15. Find the error.
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Answer: Forgot to add the y-intercept
Correct calculation: y = 3(5) + 10 = 15 + 10 = 25. Always remember both the slope term AND the y-intercept.
Question 3: A scatter plot goes down from left to right. A student says this shows a weak correlation. Is this correct?
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Answer: No - direction and strength are different properties
Going down shows NEGATIVE correlation (direction), but says nothing about strength. A tight downward pattern is a strong negative correlation.
Question 4: Data covers ages 10-18. A student uses the line of best fit to predict outcomes for a 50-year-old. What mistake is this?
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Answer: Extrapolating far beyond the data range
Predictions are only reliable within or near the range of the original data. The relationship may not hold at extreme values.
Question 5: A student draws a line through the first and last points of a scatter plot. Why is this not necessarily the line of best fit?
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Answer: The line of best fit minimizes total distance to ALL points
The first and last points might be outliers. The line of best fit considers all data points, not just endpoints.
Question 6: A residual is calculated as Predicted - Actual. What is wrong with this?
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Answer: The formula is reversed
Residual = Actual - Predicted. A positive residual means the actual point is ABOVE the line, negative means BELOW.
Question 7: A student sees r = -0.9 and says this is a weak correlation because it's negative. Correct this misconception.
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Answer: -0.9 is a STRONG negative correlation
The sign shows direction (positive or negative). The absolute value shows strength. |−0.9| = 0.9 is very strong.
Question 8: A student removes an outlier to make their line fit better. When is this appropriate vs. inappropriate?
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Answer: Only remove outliers if there's evidence of measurement error
Removing outliers just to improve fit is data manipulation. Outliers may represent real, important data points.
Question 9: The slope of a line is 2.5. A student says "y increases by 2.5 every time." What's missing from this statement?
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Answer: "...for every 1 unit increase in x"
Slope is rate of change: rise over run. You must specify the change in BOTH variables for a complete interpretation.
Question 10: A student plots (year, sales) with years 2015-2023 on x-axis. The y-intercept is negative. They say "in year 0, sales were negative." What's wrong?
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Answer: The y-intercept has no meaningful interpretation here
Year 0 is far outside the data range (extrapolation). The y-intercept is a mathematical artifact, not a meaningful prediction.