(a) enter the table into your desmos graphing calculator. find each type of regression equation and the…

(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?\nmodel\tlinear (y1~ax1 + b)\tquadratic (y1~ax1²+bx1 + c)\texponential (y1~abx1) (standard form)\nequation of regression model\ty = 0.739x - 1.071\ty=-0.013x + 1.017x - 2.193\ty = 1.477×1.057x\ncoefficient of determination\tr² = 0.919\tr² = 0.925\tr² = 0.874

(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?\nmodel\tlinear (y1~ax1 + b)\tquadratic (y1~ax1²+bx1 + c)\texponential (y1~abx1) (standard form)\nequation of regression model\ty = 0.739x - 1.071\ty=-0.013x + 1.017x - 2.193\ty = 1.477×1.057x\ncoefficient of determination\tr² = 0.919\tr² = 0.925\tr² = 0.874

Answer

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.