5 exercises · 5 automatically checked · Untimed
5 questions · Shuffled order · Untimed practice
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The model = 23 + 4.5x predicts y from x. What is its prediction when x = 8?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 59
Substitute the input: 23 + 4.5(8) = 23 + 36 = 59. The coefficient 4.5 is the rate of predicted change, not the prediction itself.
Review worked example 4.04.
An exponential model gives values 20, 40, and 80 at inputs 0, 3, and 6, respectively. Which model fits?
Answer: C: y
The value doubles every three input units, so the exponent must count groups of three: x/3. At x
Review worked example 4.11.
An observation has output 31. Its model-predicted output is 34. Using residual = observed − predicted, what is the residual?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: −3
The residual is 31 − 34
Review worked example 4.07.
Two points on a fitted line are (1, 8) and (5, 20). What output does the fitted line predict at input 7?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 26
The slope is (20 − 8)/(5 − 1)
Review worked example 4.03.
A model is fitted using observations with inputs from 10 to 30. Which statement about its prediction at input 20 is correct?
Answer: C
Twenty lies within the observed input range, making the prediction interpolation. Even within that range, the model summarizes a relationship and does not guarantee exact individual outputs or establish causation.
Review worked example 4.13.
Review Two-variable data: models and scatterplots