To determine the appropriate regression model for the dataset titled "Hours Playing with Toys," we need to analyze the nature of the relationship between age (x) and hours playing (y).
Given that the points are plotted in quadrant 1 and we have a curve, it's reasonable to assume that as age increases, the hours spent playing with toys may initially rise and then fall, leading to a parabolic shape. This suggests a downward-opening parabola.
Now, let’s analyze the given options:
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f(x) ∼ (1/12)(x - 10)² + 8: This is an upward-opening parabola since the coefficient of the squared term is positive.
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f(x) ∼ -(1/12)(x - 10)² + 8: This is a downward-opening parabola. If the vertex is at (10, 8), it suggests that there is a maximum value of 8 hours when the age is 10.
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f(x) ∼ -(1/12)(x - 8)² + 10: This is also a downward-opening parabola with its vertex at (8, 10). It suggests maximum hours of play at age 8.
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f(x) ∼ -(1/12)(x + 10)² - 8: This is a downward-opening parabola, but the vertex is at (-10, -8), which is not in quadrant 1 where the data points are.
Based on the considerations for a downward-opening parabola and the typical pattern of hours playing with toys relating to age, the most suitable choice would be one that reflects a peak amount of time spent at a realistic age for children playing with toys.
The most appropriate model seems to be:
f(x) ∼ -(1/12)(x - 10)² + 8
This equation indicates a peak at age 10 (maximum hours of 8), which fits well with developmental trends in playtime.
Thus, Jorge should create:
f(x) ∼ -(1/12)(x - 10)² + 8.