Chapter 4.5, Problem 27E

a.

To determine

To find: Equation of line of best fit using graphing calculator and to identify and interpret correlation coefficient.

Answer to Problem 27E

The equation of line of best fit is $y=-0.083x+3.83$ .

Model is a good fit for the data.

There is a strong negative correlation.

Explanation of Solution

Given Information: Table with data values of hours spent watching television and grade point average.

Calculation:

Inputting the given data in a graphing calculator, results are,

  $\begin{array}{l}\text{LinReg}\\ \text{ y=ax+b}\\ \text{ a= -0}\text{.08345323741007184}\\ \text{ b= 3}\text{.8290167865707425}\\ {\text{ r}}^2\text{= 0}\text{.930824571112341}\\ \text{ r= -0}\text{.9647925015838074}\end{array}$

As $\text{y=ax+b}$ ,

Rounding (if needed) and substituting the values,

  $y=-0.083x+3.83$

Thus, the equation of line of best fit is $y=-0.083x+3.83$ .

Interpretation:

In the graphing calculator coefficient correlation is shown by the symbol $r$ . In this case, $r=-0.96$. There is a strong negative correlation, this implies that as the students spend more time watching television their grade point average gets affected in negative way and it decreases. As the $r$ is near $-1$ , model is a good fit for the data.

b.

To determine

To interpret: The slope and $y-\mathrm{int}ercept$ of the line of best fit.

Answer to Problem 27E

The slope $0.083$ represents decrease in grade point average per hour of watching TV.

If television is not watched, grade point average would be $3.83$ .

Explanation of Solution

Given Information: Table with data values of hours spent watching television and grade point average, graphing calculator results from the previous part.

Calculation:

Interpretation:

As can be seen in graphing calculator screen, slope $(a)$ $=-0.083$ , this means that marked points make a downhill from left to right i.e. they tend to head lower and lower as we move along the horizontal axis. In the concerned case, it signifies that $0.083$ decrease in grade point average per hour of watching TV.

Putting $x=0$ in $y=-0.083x+3.83$ to calculate $y-\mathrm{int}ercept$ ,

  $y=3.83$

In this case, if television is not watched, grade point average would be $3.83$ .

c.

To determine

To approximate: Grade point average of student who watches television for given number of hours.

Answer to Problem 27E

The grade point average would be $2.668$ .

Explanation of Solution

Given Information: Given number of hours is $14$ .

Calculation:

Equation is $y=-0.083x+3.83$ ,

Putting $y=147$ in above stated equation,

  $\begin{array}{l}y=-0.083(14)+3.83\\ y=-1.162+3.83\\ y=2.668\end{array}$

Thus, the grade point average would be $2.668$ .

d.

To determine

If there is a causal relationship in given situation.

Answer to Problem 27E

Yes, there is a causal relationship.

Explanation of Solution

Given Information: Situation is about number of hours spent watching television and grade point average.

Calculation:

Yes, there is a causal relationship. If student spends more time watching television he/she would get less time for studying and he/she would remain consumed in the contents of television.