Answer:
(a) Linear: y = 2.156x + 0.391, R² = 0.9037
Quadratic: y = 0.096x² + 0.714x + 3.803, R² = 0.9485
Exponential: y = 4.626 · 1.152^x or y = 4.252e^(0.142x), R² = 0.9077
(b) The quadratic model best fits the data set because it has the greatest coefficient of determination.
Step-by-step explanation:
To use technology to find the equation and coefficient of determination (R²) for each type of regression model, we can input the given data into a regression calculator, using the number of practice throws for the input variable (x) and the number of free throws for the output variable (y).
Linear
[tex]y = 2.156x + 0.391[/tex]
[tex]R^2 = 0.9037[/tex]
Quadratic
[tex]y = 0.096x^2 + 0.714x + 3.803[/tex]
[tex]R^2 = 0.9485[/tex]
Exponential
[tex]y = 4.626 \cdot 1.152^x\quad \textsf{or}\quad y = 4.626 e^{0.142x}[/tex]
[tex]R^2 = 0.9077[/tex]
The coefficient of determination (R²) assesses the goodness of fit of a regression model, expressed as a value between 0 and 1, where a higher R-squared value indicates a better fit of the model to the data.
Therefore, the regression model that best fits the data is the quadratic model, as this model has the greatest coefficient of determination.
