Question

Using a graphing calculator or computer software package, estimate and verify the mathematical solutions for one of the following problems:

1. The following data show the commuting distances and commuting times of six college students to their college campus.

Distance in miles	2	15	16	9	21	5
Time in minutes	5	25	30	20	35	10

1. Determine the correlation coefficient between the commuting distance and the commuting time.

2. Determine whether a correlation exists at a = 0.05.

3. Determine the equation of line of best fit for the commuting distance and the commuting time.

Take a picture of your graphing calculator or a screen shot of an online calculator/software package and attach to the assignment. Please cite any extra sources, including which software you are using (graphing calculator, Excel, Desmos, etc.) Be sure to include your name on your project. Please cite all resources.

Answer 1

X: Independent variable = Distance in miles

Y: Dependent variable = Time in minutes

We can solve this question using excel.

First, enter data into excel.

Click on Data -------> Data Analysis --------> Regression ------->

Input

Input Y Range : select y values

Input X Range :select values of x.

Output Range: select an empty cell

---------> ok

We get

a)

The correlation coefficient between the commuting distance and the commuting time = r = 0.9872

b)

We have to check there is correlation between the commuting distance and the commuting time.

The null and alternative hypothesis is:

Level of significance = 0.05

Sample size = n = 6

Degrees of freedom = n - 2 = 6 - 2 = 4

Critical value = 0.754

( Using pearson critical value table)

r > critical value we reject null hypothesis.

Conclusion:

There is a correlation between the commuting distance and the commuting time.

c)

The equation of the line of best fit for the commuting distance and the commuting time is: