Question

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x | 2 | 5 | 6 | 11 | 13 | 18 | 20
y | 171 | 83 | 62 | 41 | 18 | 11 | 3
expreg: $y = a b^x$ quadreg: $y = a x^2 + b x + c$
$a = 246.084$ $a = 0.700$
$b = 0.821$ $b = -23.225$
$c = 196.583$
$r^2 = 0.946$ $r^2 = 0.935$
which regression model more closely fits the data?

• expreg (exponential)
• quadreg (quadratic)

(c) write the equation of the model that best fits the data. write the values in your answer to 3 decimal places.

Explanation:

Step1: Identify the best - fit model

We know that the coefficient of determination \(R^{2}\) is used to determine how well a regression model fits the data. A higher \(R^{2}\) value indicates a better - fitting model. For the exponential regression model (ExpReg), \(R^{2}=0.946\), and for the quadratic regression model (QuadReg), \(R^{2} = 0.935\). Since \(0.946>0.935\), the exponential regression model (ExpReg) is the best - fit model.

Step2: Write the equation of the ExpReg model

The general form of the exponential regression model is \(y = a\cdot b^{x}\). From the given data, we have \(a = 246.084\) and \(b=0.821\). Substituting these values into the general form of the exponential regression equation, we get the equation of the best - fit model.

Answer:

The equation of the model that best fits the data is \(y = 246.084\times(0.821)^{x}\)