To choose the appropriate regression model from the given options, we need to consider the characteristics of the data that Jorge has plotted on the graph. Since it appears that there is a curve plotted in quadrant 1, it suggests that the relationship between age (x-axis) and hours (y-axis) may be quadratic in nature.
Let's analyze the options based on their forms:
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f(x)∼−112(x+10)2−8: This is a downward-opening parabola (since it has a negative coefficient), with its vertex at (-10, -8). This may not be appropriate since both age and hours should be positive.
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f(x)∼−112(x−8)2+10: This is also a downward-opening parabola, with its vertex at (8, 10). This could be valid depending on whether the graph shows a peak in that region but still has a negative opening which might not fit if we expect to see hours increasing with age initially.
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f(x)∼−112(x−10)2+8: This is a downward-opening parabola with a vertex at (10, 8). Similar reasoning applies as for the previous option; it's negative but does have a peak at a reasonable positive point.
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f(x)∼112(x−10)2+8: This is an upward-opening parabola (positive coefficient), with a vertex at (10, 8). This would imply that the hours played with toys increase as age increases, which may reflect typical behavior in early childhood where younger children might spend more time playing with toys before it declines.
Given these explanations, if Jorge observed that younger children spend more hours playing with toys (a common trend), then the upward-opening curve would make sense.
Thus, the most appropriate regression model for Jorge to create is:
f(x)∼112(x−10)2+8, indicating a positive trend as age increases.