Question
Use the image to answer the question.
On a graph titled Hours Playing with Toys, a curve and twenty points are plotted in quadrant 1 of a coordinate plane. The x-axis is labeled Age, and the y-axis is labeled Hours.
Jorge needs to create an appropriate regression model given the bivariate dataset. Which of the following should he create?
(1 point)
Responses
f(x)∼−112(x+10)2−8
f left parenthesis x right parenthesis is similar to negative Start Fraction 1 over 12 End Fraction left parenthesis x plus 10 right parenthesis squared minus 8
f(x)∼−112(x−8)2+10
f left parenthesis x right parenthesis is similar to negative Start Fraction 1 over 12 End Fraction left parenthesis x minus 8 right parenthesis squared plus 10
f(x)∼−112(x−10)2+8
f left parenthesis x right parenthesis is similar to negative Start Fraction 1 over 12 End Fraction left parenthesis x minus 10 right parenthesis squared plus 8
f(x)∼112(x−10)2+8
On a graph titled Hours Playing with Toys, a curve and twenty points are plotted in quadrant 1 of a coordinate plane. The x-axis is labeled Age, and the y-axis is labeled Hours.
Jorge needs to create an appropriate regression model given the bivariate dataset. Which of the following should he create?
(1 point)
Responses
f(x)∼−112(x+10)2−8
f left parenthesis x right parenthesis is similar to negative Start Fraction 1 over 12 End Fraction left parenthesis x plus 10 right parenthesis squared minus 8
f(x)∼−112(x−8)2+10
f left parenthesis x right parenthesis is similar to negative Start Fraction 1 over 12 End Fraction left parenthesis x minus 8 right parenthesis squared plus 10
f(x)∼−112(x−10)2+8
f left parenthesis x right parenthesis is similar to negative Start Fraction 1 over 12 End Fraction left parenthesis x minus 10 right parenthesis squared plus 8
f(x)∼112(x−10)2+8
Answers
Answered by
GPT-4o mini
To determine the most appropriate regression model for Jorge based on the description of the graph, we can analyze the possible options given:
1. The options include quadratic functions, which are indicated by the presence of the squared term in the formula. This suggests that the data has a parabolic trend.
2. Given that the x-axis represents age (which typically increases) and the y-axis represents hours spent playing with toys, we might expect a peak in toy playtime at certain ages before it declines, which is indicative of an inverted parabola (opening downwards).
3. The options with a negative coefficient for the squared term (-1/12) would suggest a function that opens downward, while the positive coefficient (1/12) suggests a function that opens upward.
Since we are looking for a model that captures a peak in hours played as children age, the function should have a negative leading coefficient.
Therefore, the appropriate choice from the options provided would be:
**f(x)∼−112(x−8)2+10**
This model suggests that at age 8, the maximum number of hours spent playing with toys is around 10 hours, followed by a decrease as children age further, aligning with the typical behavior of children and their playtime as they grow older.
1. The options include quadratic functions, which are indicated by the presence of the squared term in the formula. This suggests that the data has a parabolic trend.
2. Given that the x-axis represents age (which typically increases) and the y-axis represents hours spent playing with toys, we might expect a peak in toy playtime at certain ages before it declines, which is indicative of an inverted parabola (opening downwards).
3. The options with a negative coefficient for the squared term (-1/12) would suggest a function that opens downward, while the positive coefficient (1/12) suggests a function that opens upward.
Since we are looking for a model that captures a peak in hours played as children age, the function should have a negative leading coefficient.
Therefore, the appropriate choice from the options provided would be:
**f(x)∼−112(x−8)2+10**
This model suggests that at age 8, the maximum number of hours spent playing with toys is around 10 hours, followed by a decrease as children age further, aligning with the typical behavior of children and their playtime as they grow older.
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