Chapter 1.3, Problem 17E

To determine

To find: An equation of the line of best fit using linear regression feature of a graphing calculator, then to estimate annual tuition in $2020$ and then at last interpret slope and $\text{y-intercept}$ .

Answer to Problem 17E

The average annual tuition fees in $2020$ would be about $\$16991$ . Slope signifies that tuition increases by Y $\$380$ per year. 1 $\text{y-intercept}$ implies that annual tuition in 3

$2005$ would have been near about $\$11290$ .

Explanation of Solution

Given information: Relevant data-values are given.

Calculation:

Using the linear regression feature of the graphing utility,

$\begin{array}{l}\text{LinReg}\\ \text{ y=ax+b}\\ \text{ a= 380}\text{.0285714285714}\\ \text{ b= 11290}\text{.095238095239}\\ {\text{ r}}^2\text{= 0}\text{.9737054984202163}\\ \text{ r= 0}\text{.9867651688320865}\end{array}$

Rounding the values (if needed) and substituting in the standard form,

Equation is $y=380.03x+11290.1$

Putting $x=15$ in above stated equation,

$\begin{array}{l}y=380.03(15)+11290.1\\ \\ y=5700.45+11290.1\\ \\ y=16990.55\end{array}$

Thus, the average annual tuition fees in $2020$ would be about $\$16991$ .

Graph:

Interpretation:

Slope signifies that tuition increases by near about $\$380$ every year and value of $\text{y-intercept}$ implies that as per equation of line of best fit annual tuition in year $2005$ would have been near about $\$11290$ .