Problem-Solving and Data AnalysisMediumComputing a residual
Problem-Solving and Data Analysis practice question
For a set of data, the line of best fit is y = 3x + 5. One data point in the set has coordinates (4, 20). What is the difference between the actual y-value of this point and the y-value predicted by the line?
Answer: 3
The line predicts y = 3(4) + 5 = 17 at x = 4. The actual value is 20, so the difference is 20 − 17 = 3. (The point lies 3 units above the line.)
Common wrong answers
- If you answered 16
- 16 is 20 − 4, subtracting the x-coordinate. Compare the actual y with the predicted y, 17.
- If you answered 17
- 17 is the PREDICTED value. The question asks how far the actual value, 20, is from it.
- If you answered -3
- −3 has the sign reversed: actual minus predicted is 20 − 17 = +3.
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