Question

(a) enter the table into your desmos graphing calculator. find each type of regression equation and the coefficient of determination. round to 3 decimal places if necessary. (b) which model best represents this data set?
model\tlinear (y1~ax1 + b)\tquadratic (y1~ax1²+bx1 + c)\texponential (y1~abx1) (standard form)
equation of regression model\ty = 0.739x - 1.071\ty=-0.013x + 1.017x - 2.193\ty = 1.477×1.057x
coefficient of determination\tr² = 0.919\tr² = 0.925\tr² = 0.874

Explanation:

Step1: Recall coefficient - of - determination concept

The coefficient of determination $r^{2}$ measures how well the regression model fits the data. The closer $r^{2}$ is to 1, the better the model fits the data.

Step2: Compare $r^{2}$ values

We have $r^{2}=0.874$ for the exponential model, $r^{2}=0.925$ for the quadratic model, and $r^{2}=0.919$ for the linear model.

Step3: Determine the best - fitting model

Since $0.925>0.919 > 0.874$, the quadratic model has the highest coefficient of determination.

Answer:

The quadratic model best represents the data set.