Question

The data set shows the number of practice free throws players in a basketball competition made and the number of free throws they made in a timed competition.
Practice throws 3 12 6 14 2 7 10 8
Free throws 10 22 9 35 4 11 28 20

A. Use technology to find the equation AND coefficient of determination for each type of regression model. Use the number of practice throws for the input variable and the number of free throws for the output variable. Round all decimal values to three places.
B. EXPLAIN, using the information you found above, which model best fits the data set. How did you come to your conclusion?

Answer 1

Answer-

The exponential model best fits the data set.

Solution-

x = input variable = number of practice throws

y = output variable =  number of free throws

Using Excel, Linear, Quadratic and Exponential regression model were generated.

The best fit equation and co-efficient of determination R² are as follows,

Linear Regression  

Quadratic Regression

Exponential Regression

The value of co-efficient of determination R² ranges from 0 to 1, the more closer its value to 1 the better the regression model is.

Now,

Therefore, the Exponential Regression model must be followed.