Construct a Scatterplot and Identify the Mathematical Model That Best

question 75

Multiple Choice

Construct a scatterplot and identify the mathematical model that best fits the data. Assume that the model is to be used only for the scope of the given data and consider only linear, quadratic, logarithmic, exponential, and power models. Use a calculator or computer to obtain the regression equation of the model that best fits the data. You may need to fit several
models and compare the values of R²
- $\begin{array} { c c c c } \mathrm { Y } & \mathrm { X } _ { 1 } & \mathrm { X } _ { 2 } & \\ 98.6 & 87.4 & 108.5 & \\ 101.2 & 97.6 & 110.1 & \\ 102.4 & 96.7 & 110.4 & \text { CORRELATION COEFFICIENTS } \\ 100.9 & 98.2 & 104.3 & \\ 102.3 & 99.8 & 107.2 & \mathrm { Y } / \mathrm { X } _ { 1 } = .850 \\ 101.5 & 100.5 & 105.8 & \mathrm { Y } / \mathrm { X } _ { 2 } = .742 \\ 101.6 & 103.2 & 107.8 & \\ 101.6 & 107.8 & 103.4 & \\ 99.8 & 96.6 & 102.7 & \text { COEFFICIENT OF DETERMINATION } \\ 100.3 & 88.9 & 104.1 & \\ 97.6 & 75.1 & 99.2 & \mathrm { Y } / \mathrm { X } _ { 1 } = .723 \\ 97.2 & 76.9 & 99.7 & \mathrm { Y } / \mathrm { X } _ { 2 } = .550 \\ 97.3 & 84.6 & 102.0 & \mathrm { Y } / \mathrm { X } _ { 1 } , \mathrm { X } _ { 2 } = .867 \\ 96.0 & 90.6 & 94.3 & \\ 99.2 & 103.1 & 97.7 & \\ 100.3 & 105.1 & 101.1 & \\ 100.3 & 96.4 & 102.3 & \\ 104.1 & 104.4 & 104.4 & \\ 105.3 & 110.7 & 108.5 & \\ 107.6 & 127.1 & 111.3 & \end{array}$

• A) \(\hat { Y } = 52.6 + .462 X _ { 2 }\)
• B) \(\hat { Y } = 58.9 + .612 X _ { 1 }\)
• C) \(\hat { \mathrm { Y } } = 48.0 + .398 \mathrm { X } _ { 1 } + .228 \mathrm { X } _ { 2 }\)
• D) \(\hat { \mathrm { Y } } = 57.6 + .153 \mathrm { X } _ { 1 } + .270 \mathrm { X } _ { 2 }\)

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Definitions:

Nerve Impulse

Electrical signal that conveys information along the length of a neuron.

Neuron Membrane

The lipid bilayer that encloses the cytoplasm of neurons, crucial for nerve impulse transmission.

Potassium Ions

Essential positive ions (K+) within cellular processes, crucial for nerve function, muscle contraction, and maintaining fluid and electrolyte balance.

Cerebrum

The largest part of the brain, responsible for voluntary actions, sensory perception, thought, reasoning, and memory.