Guided Practice
Overview
This lesson provides structured practice with scatter plots and lines of best fit. Work through each problem step-by-step, applying the techniques you learned in the previous lessons.
Practice Problems
Question 1: A scatter plot shows hours studied (x) vs. test scores (y). The points appear to rise from left to right. What type of correlation does this show?
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Answer: Positive correlation
When points rise from left to right, as x increases, y also increases, indicating a positive relationship between the variables.
Question 2: Given points (2, 4), (4, 7), (6, 10), and (8, 13), estimate the slope of the line of best fit.
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Answer: Slope is approximately 1.5
Using two points: (8-2)/(13-4) = 6/9 = 1.5. This can also be seen as y increasing by about 3 for every increase of 2 in x.
Question 3: A line of best fit has equation y = 2.5x + 10. Predict the y-value when x = 12.
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Answer: y = 40
Substitute x = 12: y = 2.5(12) + 10 = 30 + 10 = 40.
Question 4: Points are scattered randomly with no pattern. What can you conclude about the correlation?
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Answer: No correlation (correlation near 0)
When points show no pattern, there is no linear relationship between the variables.
Question 5: The line of best fit for a data set is y = -3x + 50. What does the negative slope tell you?
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Answer: Negative correlation - as x increases, y decreases
A negative slope means the variables have an inverse relationship; when one goes up, the other goes down.
Question 6: A scatter plot has most points clustered tightly around a line. Is the correlation strong or weak?
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Answer: Strong correlation
When points are close to the line of best fit, the correlation is strong because the linear model fits the data well.
Question 7: Given the equation y = 0.8x + 5, what is the y-intercept and what does it mean?
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Answer: The y-intercept is 5
This means when x = 0, the predicted y-value is 5. In context, it represents the starting value before x has any effect.
Question 8: A point (5, 20) lies far above the line of best fit y = 2x + 3. What is this point called?
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Answer: An outlier
The line predicts y = 2(5) + 3 = 13, but the actual value is 20. Points that deviate significantly from the pattern are called outliers.
Question 9: Using y = 1.5x + 8, calculate the residual for the point (4, 15).
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Answer: Residual = 1
Predicted: y = 1.5(4) + 8 = 14. Residual = Actual - Predicted = 15 - 14 = 1.
Question 10: Two scatter plots show the same data. One uses a linear model, one uses a curved model. The curved model has smaller residuals overall. Which model is better?
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Answer: The curved model is better for this data
Smaller residuals indicate the model fits the data more accurately. Sometimes data has a non-linear pattern.