Chapter PII, Problem 37RE

(a)

To determine

To find the predicted value of y using each model for $x=10$ .

Answer to Problem 37RE

The value of yis $3.8421$ .

Explanation of Solution

Now, in this question we have to predict value of y using each model for $x=10$ . The equation is:

  $\widehat{y}=2+0.8\ln x$

Now, we will solve the equation as:

  $\begin{array}{l}\widehat{y}=2+0.8\ln x\\ =2+0.8\ln (10)\\ =3.8421\end{array}$

(b)

To determine

To find the predicted value of y using each model for $x=10$ .

Answer to Problem 37RE

The value of yis $501.187$ .

Explanation of Solution

Now, in this question we have to predict value of y using each model for $x=10$ . The equation is:

  $\log \widehat{y}=5-0.23x$

Now, we will solve the equation as:

  $\begin{array}{l}\log \widehat{y}=5-0.23x\\ \Rightarrow \log \widehat{y}=5-0.23(10)\\ \Rightarrow \log \widehat{y}=2.7\\ \Rightarrow \widehat{y}={10}^{2.7}\\ \Rightarrow \widehat{y}=501.187\end{array}$

(c)

To determine

To find the predicted value of y using each model for $x=10$ .

Answer to Problem 37RE

The value of yis $4$ .

Explanation of Solution

Now, in this question we have to predict value of y using each model for $x=10$ . The equation is:

  $\frac{1}{\sqrt{\widehat{y}}}=17.1-1.66x$

Now, we will solve the equation as:

  $\begin{array}{l}\frac{1}{\sqrt{\widehat{y}}}=17.1-1.66x\\ \Rightarrow \frac{1}{\sqrt{\widehat{y}}}=17.1-1.66(10)\\ \Rightarrow \sqrt{\widehat{y}}=\frac{1}{0.5}\\ \Rightarrow \widehat{y}=2^2\\ \Rightarrow \widehat{y}=4\end{array}$