Chapter 1.6, Problem 24PPE

(a)

To determine

To describe: The accuracy of the line.

Explanation of Solution

Given:

The graph of the mass of marbles is shown in Figure 1.

  

Figure 1

Each point on the graph shows the relation between the number of marble and its mass where the number of marbles is the independent variable and the mass is dependent variable.

The accuracy of the line depends on the closeness of the points to the line.

It can be seen from the given graph that some points are above the line and some are below the line and some are passing through.

The points are close to the line. Therefore, there is high positive correlation but not a perfect correlation.

The points are close to the line but all points do not pass through the line. In conclusion accuracy is quite good but not perfectly correct.

(b)

To determine

To find: The approximate mass of 7 marbles.

Answer to Problem 24PPE

The approximate mass of 7 marbles is 1.1g.

Explanation of Solution

Given:

The graph of the mass of marbles is shown in Figure 1.

  

Figure 1

The number of marbles is shown on the horizontal axis that is independent variable and the mass is shown on the vertical axis that is dependent variable.

See the point for 7 marbles on the graph.

It can be observed from Figure 1 that the approximate mass of 7 marbles is 1.1g.

Therefore, the approximate mass of 7 marbles is 1.1g.

(c)

To determine

To explain: The reason of few points is above the line and some are below the line.

Explanation of Solution

Given:

The graph of the mass of marbles is shown in Figure 1.

  

Figure 1

The set of points are the scatter plot of the line that make predictions to make a best fit line.

The line of best fit is the line passes through the points or closely to the point. If half of the data points on the scatter point is below the line and half above the line.

It can be seen from Figure 1 that the data points come close to the line of the best fit that means the correlation is the strong.

The positive correlation is high since it predicts the values near the line some points are above the line and some are below the line.

(d)

To determine

To make: A conjecture for the approximate mass of 20 marbles and explain the reasoning.

Explanation of Solution

Given:

The graph of the mass of marbles is shown in Figure 1.

  

Figure 1

It can be observed from the Figure 1 that the possible set of points are represented in the below table.

Number of marbles	Mass
0	0
2	0.38
3	0.5
5	0.7
7	1.1
9	1.3
10	1.48

It can be seen that that the line of the regression is the form of $a+bx$ .

The point is 1.48 at the time of 10 marbles.

Therefore, there is possibility of the slope is 1.433 and the y- intercept is 0.05 something.

Substitute 1.433 for $a$ and 0.05 for $b$ in the equation to obtain the equation.

  $y=1.433+0.05x$

Take these points for the line to make a conjecture for the 20 marbles.

Substitute 20 for $x$ in the equation $y=0.1433+0.05x$ to obtain the value of 20 marbles.

  $\begin{array}{c}y=1.433+0.05\left(20\right)\\ =1.433+1\\ =2.433\end{array}$

Therefore, it would be 2.433 something.