Question

HELP PLS!! NEED THIS ASAP!!!!

Answer 1

`\begin{array}{l}\sf a)\\\\\\\\\\\\\end{array}\begin{array}c\cline{1-3}\vphantom{\frac12}\sf Model & \textsf{Equation of regression model}&\textsf{Coefficient of determination}\\\cline{1-3}\vphantom{\frac12}\sf Linear & y=2.334x-1.098 & 0.853\\\cline{1-3}\vphantom{\frac12}\sf Quadratic & y = 0.134x^2 + 0.405x + 3.327 & 0.918\\\cline{1-3}\vphantom{\frac12}\sf Exponential & y=3.729\cdot 1.178^x&0.899\\\cline{1-3}\end{array}`

b) Quadratic model

Explanation:

Using a graphical calculator, the equations and coefficients of determination (R-squared) of each type of regression model are:

Linear

`\textsf{Equation:}\quad y=2.334x-1.098`

`\textsf{Coefficient of determination:}\quad 0.853`

Quadratic

`\textsf{Equation:}\quad y = 0.134x^2 + 0.405x + 3.327`

`\textsf{Coefficient of determination:}\quad 0.918`

Exponential

`\textsf{Equation:}\quad y=3.729\cdot 1.178^x`

`\textsf{Coefficient of determination:}\quad 0.899`

The coefficient of determination, often denoted as R-squared (R²), is a statistical measure used to assess the goodness of fit of a regression model. It is expressed as a value between 0 and 1. A greater R-squared value indicates a better fit of the regression model to the data.

Therefore, the model that best fits the data is the quadratic model, as this model has the greatest coefficient of determination.