Chapter 10, Problem 18E

(a)

To determine

To construct: length of the year vs. the distancefrom the sun and explain the shape of the plot.

Explanation of Solution

Given:

  

Graph:

Scatter Plot:

  

The scatter plot indicates a relationship that is moderate to powerful, positive and upward curved. The Planethave longer years away from the sun than closer planets.

(b)

To determine

To Explain: In order to straighten the plot and justify the duration of a planet's year depending on its distance from the sun, it re-expresses either or both variables.

Explanation of Solution

Given:

  

Calculation:

Distance from sun	Length of year	Log(distance from sun)	log (length of year)
36	0	1.5563	-0.6198
67	1	1.8261	-0.2147
93	1	1.9685	0.0000
142	2	2.1523	0.2742
484	12	2.6848	1.0741
887	29	2.9479	1.4692
1784	84	3.2514	1.9246
2796	165	3.4465	2.2170
3707	248	3.5690	2.3939

Graph:

Scatter Plot:

  

  

From the result of the regression line $\log \left(length\right)=-2.95+1.50\text{Distance}$ . R-squared of the model is 100 percent it implies 100 percent of variability in the log of length is estimated for by the model.

(c)

To determine

To Explain: the model for the fits the data.

Explanation of Solution

Given:

  

The model's R-squared is 100%, indicating that the model accounts for 100% variability in the log (length). No pattern displays the residual plot. So, it suits well with the linear model.