Chapter 4.4, Problem 22PFA

a.

To determine

To graph: The scatter plot of the data. And draw a line of fit.

Explanation of Solution

Given:

The table below shows the change in sea level over 50 year period.

  

Graph:

Plot the points of the scattered plot using the data from the above table, where x is the year and y is the change in sea level.

  

Conclusion:

b.

To determine

To identify: Whether the scatter plot shows positive, negative or no correlation.

Answer to Problem 22PFA

The scatter plot shows Positive correlation.

Explanation of Solution

Given:

Scatter plot is given in subpart a.

Concept Used:

From the scatter plot it can see that the best line of fit has positive slope.

Conclusion:

So, it can conclude that the scatter plot has positive correlation.

c.

To determine

To write: The equation for the line of best fit passing through the points (1970,5.6) and (1995,7.3).

Answer to Problem 22PFA

The equation for the line of best fit passing through the points is $1.7x-25y-3209=0$ .

Explanation of Solution

Given:

The points lying on the line of best fit are given as (1970,5.6) and (1995,7.3).

Calculation:

Equation of a line in two-point form is given by,

  $\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}$

So, from the given points $x_1=1970,y_1=5.6,x_2=1995,y_2=7.3$

So, the equation of the line of best fit passing through the points (1970,5.6) and (1995,7.3) will be,

  $\begin{array}{l}\frac{y-5.6}{7.3-5.6}=\frac{x-1970}{1995-1970}\\ \therefore \frac{y-5.6}{1.7}=\frac{x-1970}{25}\\ \therefore 25y-140=1.7x-3349\\ \therefore 1.7x-25y-3349+140=0\\ \therefore 1.7x-25y-3209=0\dots (1)\end{array}$

Conclusion:

d.

To determine

To Find: The best prediction of change in sea level in 2030.

Answer to Problem 22PFA

The best prediction of change in sea level in 2030 is C. 9.7inches.

Explanation of Solution

Given:

The year is given as 2030. The equation of the line of best fit is given by equation (1) as $1.7x-25y-3209=0$ .

Calculation:

Now, find y for $x=2030$ .

So, plug-in $x=2030$ in equation 1.

  $\begin{array}{l}\therefore 1.7(2030)-25y-3209=0\\ \therefore 3451-25y-3209=0\\ \therefore -25y+242=0\\ \therefore -25y=-242\\ \therefore y=\frac{-242}{-25}\\ \therefore y=9.68\end{array}$

  $\Rightarrow y\approx 9.7$