Chapter 12, Problem 6CRE

(a)

To determine

To construct: the residual figure.

Explanation of Solution

Given:

  

Graph:

  

The residual is negative if the point is under the blue regression line. If the point is above the blue regression line, the value is positive. The exact value of the residual is the vertical distance to the blue line. The residual plot is having time values on the horizontal axis and the rest are on the vertical axis. There is then above a probable residual plot.

(b)

To determine

To Explain: the reason that a linear model is not suitable for explaining the association between percent of words recalled and practise time.

Answer to Problem 6CRE

Not appropriate

Explanation of Solution

Given:

  

By seeing the plot, it is observed that A linear model is not suitable, because the scatter plot has a curvature and the residual plot has a clear pattern.

(c)

To determine

To find: that would a power model or an exponential model explain the relationship better, Explain the answer.

Answer to Problem 6CRE

Power Model

Explanation of Solution

Given:

  

The top scatterplot plot is a power model (both of these variables are in), where the bottom scatterplot plot refers to an exponential model. The model which best explains the relation has by far the most linear pattern in the scatterplot.

(d)

To determine

To find: word recall estimation for 25 seconds of Part (c) practise.

Answer to Problem 6CRE

Word recalled $y=83.3568$

Explanation of Solution

Given:

  

Calculation:

Regression equation for the top scatterplot:

  $\ln y\text{=3}\text{.48+0}\text{.293}\ln x$

Where the $x$ is the time and $y$ is the recall.

Putting the value of $x$ =25

  $\begin{array}{c}\ln y\text{=3}\text{.48+0}\text{.293}\ln x\\ \ln y\text{=3}\text{.48+0}\text{.293}\ln \left(25\right)\\ =4.42313\end{array}$

Taking the exponential

  $\begin{array}{c}y=e^{4.42313}\\ =83.3568\end{array}$