a. Find a power function that models the data below.
b. Find a linear function that models the data
c. Visually determine which model is a better fit.
0
х
y
1
2
2
7
3
13
4
22
5
32
6
44
a. The power function is y=0
(Use integers or decimals for any numbers in the expression. Round to the nearest thousandth as needed)

Question

01-10-2021
Mathematics

contestada

a. Find a power function that models the data below.
b. Find a linear function that models the data
c. Visually determine which model is a better fit.
0
х
y
1
2
2
7
3
13
4
22
5
32
6
44
a. The power function is y=0
(Use integers or decimals for any numbers in the expression. Round to the nearest thousandth as needed)

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fichoh fichoh · Answer 1 · 2021-10-13T16:32:03+02:00

Using Visual inspection, the model which fits the data in the distribution better is the power function.

The power and linear functions can of the data can both be modeled using technology,

Using Technology :

The power function in the form [tex] y = Ax^{B} [/tex] which models the data is [tex] 1.926x^{1.662} [/tex]

The linear function in the form [tex]y = Bx + A [/tex] which models the data is [tex] y = 7.429x - 8.333[/tex]

Where A = intercept and B = slope

From the model, correlation coefficient given by the power and linear models are 0.999 and 0.986 respectively.

Hence, the power model is a better fit for the data than the linear model.

Therefore, Inspecting the models visually, the power function fits the data better as the points on the curve are closer to the regression line than on the linear model.

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