Chapter 12, Problem 45PT4

a)

To determine

To explain the relationship using scatter plot.

Answer to Problem 45PT4

The relationship between two variables is strong curvature.

Explanation of Solution

Given:

  

The relationship between two variables is strong curvature. Therefore, it is not linear relationship. Also, there appears to be one outlier at rightmost point.

b)

To determine

To identify which model predicts better.

Answer to Problem 45PT4

Model B.

Explanation of Solution

Given:

  

  

  

  

The scatter plot and residual plot of Model A shows strong curvature as compare to Model B. Also, the residuals in the residual plot of Model B shows randomly scattered. Hence, Model B gives better prediction.

c)

To determine

To predict the seed weight if the seed count is 3700 using model B.

Answer to Problem 45PT4

The predicted seed weight is 19.7766 mg.

Explanation of Solution

Given:

  

Formula:

The general linear regression equation,

  $\widehat{y}=b_0+b_{1}x$

From given model,

  $\begin{array}{l}{b}_0=15.491\\ b_1=-1.5222\end{array}$

Therefore, the model is,

  $\ln (weight)=15.491-1.5222\ln (count)$

Put count = 3700

  $\begin{array}{l}\ln (weight)=15.491-1.5222\ln (3700)\\ weight=e^{\ln (weight)}=e^{2.9845}\approx 19.776\end{array}$

Hence, the predicted seed weight is 19.7766 mg.

d)

To determine

To interpret the value of r².

Answer to Problem 45PT4

The 86.3% of the variation in ln(weight) is explained by the linear model.

Explanation of Solution

Given:

  

The R-square is the percentage of variation in dependent variable explained by the model.

The R-square = 86.3%. Therefore, the 86.3% of the variation in ln(weight) is explained by the linear model.