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QuizMultiple Choice

Regression Models — Quiz

Question 1 • Algebraic Reasoning

The data in the table represents a company's profit based on the number of items produced. Profit Based on Number of the Items Produced Items Produced x Dollars of profit y 100 negative 70 comma 500 200 50 300 50 comma 100 400 80 comma 300 500 90 comma 400 600 78 comma 000 Which equation best represents the data?

Answer
A
y is equal to negative 1 point 0 3 6 x squared plus 1024 point 7 7 1 x minus 163710
B
y is equal to negative 1 point 0 2 6 x squared plus 1016 point 4 0 2 x minus 162075
C
y is equal to 298 point 2 1 4 x minus 66317 point 6 6 7
D
y is equal to 196 point 2 x minus 18710

Explanation

Choice B gives values close to the table’s profits. For example, when x = 300, it predicts y = −1.026(300²) + 1016.402(300) − 162075 = 50,505.6, close to the listed $50,100. At x = 400, it predicts about $80,326, close to $80,300. The small differences are expected because the equation is a best-fit model.

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