Chapter EP, Problem 2.5.3EP

(a)

To determine

To find:The scatter plot and a line of fit and correlation.

Answer to Problem 2.5.3EP

The scatter plot and a line of fit and correlation are discussed.

Explanation of Solution

Given:

The table of data is given.

Calculation:

Plot the graph by plotting the years on horizontal axis and population on vertical axis.

The points are (10, 4.25) and (16, 5.15).

These points fit the data well.

The scatter plot shows the strong positive correlation.

Thus, the scatter plot and a line of fit and correlation are discussed.

(b)

To determine

To find:The prediction equation.

Answer to Problem 2.5.3EP

The prediction equation is $y=0.15x+2.75$

Explanation of Solution

Given:

The table of data is given.

Calculation:

Calculate the slope.

  $\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{5.15-4.25}{16-10}\\ =0.15\end{array}$

The equation of line is given as,

  $\left(y-y_1\right)=m\left(x-x_1\right)$

Substitute the values.

  $\begin{array}{l}\left(y-y_1\right)=m\left(x-x_1\right)\\ \left(y-4.25\right)=0.15\left(x-10\right)\\ y=0.15x+2.75\end{array}$

Thus, the prediction equation is $y=0.15x+2.75$

(c)

To determine

To find:The missing value.

Answer to Problem 2.5.3EP

The missing value is $7.85$ .

Explanation of Solution

Given:

The table of data is given.

Calculation:

Substitute the values.

  $\begin{array}{c}y=0.15x+2.75\\ =0.15\left(34\right)+2.75\\ =7.85\end{array}$

Thus, the missing value is $7.85$ .