# 12.8: Regression (Distance from School)

- Page ID
- 803

[ "article:topic", "OpenStax", "authorname:openstax" ]

Name: ______________________________

Section: _____________________________

Student ID#:__________________________

*Work in groups on these problems. You should try to answer the questions without referring to your textbook. If you get stuck, try asking another group for help.*

### Student Learning Outcomes

- The student will calculate and construct the line of best fit between two variables.
- The student will evaluate the relationship between two variables to determine if that relationship is significant.

### Collect the Data

Use eight members of your class for the sample. Collect bivariate data (distance an individual lives from school, the cost of supplies for the current term).

- Complete the table.
**Distance from school****Cost of supplies this term** - Which variable should be the dependent variable and which should be the independent variable? Why?
- Graph “distance” vs. “cost.” Plot the points on the graph. Label both axes with words. Scale both axes.
**Figure 12.8.1.**

### Analyze the Data

Enter your data into your calculator or computer. Write the linear equation, rounding to four decimal places.

- Calculate the following:
- \(a =\) ______
- \(b =\) ______
- correlation = ______
- \(n =\) ______
- equation: \(\hat{y} =\) ______
- Is the correlation significant? Why or why not? (Answer in one to three complete sentences.)

- Supply an answer for the following senarios:
- For a person who lives eight miles from campus, predict the total cost of supplies this term:
- For a person who lives eighty miles from campus, predict the total cost of supplies this term:

- Obtain the graph on your calculator or computer. Sketch the regression line.
**Figure 12.8.2.**

### Discussion Questions

- Answer each question in complete sentences.
- Does the line seem to fit the data? Why?
- What does the correlation imply about the relationship between the distance and the cost?

- Are there any outliers? If so, which point is an outlier?
- Should the outlier, if it exists, be removed? Why or why not?