Chapter 3.4, Problem 27AYU

Which Model? The following data represent the square footage and rents (dollars per month) for apartments in the La Jolla area of San Diego, California.

(a) Using a graphing utility, draw a scatter diagram of the data treating square footage as the independent variable. What type of relation appears to exist between square footage and rent?

(b) Based on your response to part (a), find either a linear or a quadratic model that describes the relation between square footage and rent.

(c) Use your model to predict the rent for an apartment in San Diego that is 875 square feet.

To determine

To calculate:

a. Graph a scattered diagram and determine the type of relation that exists between the 2 variables.

b. Find the equation of best fit.

c. Predict the rent for an apartment in the city that is 875 square feet.

Answer to Problem 27AYU

a. The graph is given below.

b. The equation of best fit is $y=1.229x+917.38$.

c. The rent for an 875 square foot apartment will be $\$1992.75$.

Explanation of Solution

Given:

The given data represents the relation between the square footage and the rents for apartments of San Diego.

Formula used:

For a quadratic equation $y=a{x}^2+bx+c,$ if $a$ is positive, then the vertex $\left(\frac{-b}{2a},<mtext> </mtext>y\left(\frac{-b}{2a}\right)\right)$ is the minimum point and if $a$ is negative, the vertex $\left(\frac{-b}{2a},<mtext> </mtext>y\left(\frac{-b}{2a}\right)\right)$ is the maximum point.

Calculation:

We can draw the scatter diagram using Microsoft Excel.

Thus, on entering the $x$ and the $y$ values on excel, we have to choose the Scatter diagram form the insert option.

Then for getting the equation of best fit, we have to choose the Layout option and then Trendline and then more Trendline option. Then choose the option polynomial and then display the equation.

Thus, we get the scatter diagram with the equation of best fit as

a. The scatter diagram is drawn above and we can see that the given variables exhibit a linear relationship with positive slope.

b. The equation of best fit is $y=1.229x+917.38$

c. When $x=875,$ we get

$y(875)=1.229(875)+917.38=1992.75$

The rent for an 875 square foot apartment will be $\$1992.75$.