LAB MODULE 9

LINEAR REGRESSION

PURPOSE

The purpose of this activity is to determine which variable best predicts the height of a person. You'll use your knowledge of scatterplots, correlation, and regression to complete the assignment.

OUTCOMES YOU'LL MEET

The course outcomes you'll meet are....

The instructional goal is to look for relationships between two variables:

1. Identify response and explanatory variables.
2. Construct a scatterplot.
3. Determine whether the two variables have a positive or negative association.
4. Calculate and interpret the correlation coefficient, r , and the coefficient of determination, r² .
5. Calculate and interpret the least-squares regression line using technology
6. Predict values of the dependent variable using the least-squares regression line

BACKGROUND

In a statistics class, last spring, the students measured their height, their arm span (finger tip to finger tip), and the length of their forearm (elbow to finger tip). All distances were measured in inches.

We collected data to answer this question: Which is a better predictor of someone's height, their arm span, or their forearm length?

In other words, will someone's forearm length or their arm span more accurately predict their height?

Listed below are the data that were collected.

TABLE OF DATA: MEASUREMENTS FROM STUDENTS
Student	Arm span	Forearm length	Height
A	60.5	16	62
B	68	17.5	67
C	60	16.6	61
D	64.5	17	65
E	63.5	17	62.5
F	61.5	16.5	62.5
G	67	18	68
H	67	18.5	71.5

TO DO:

Use your skills from this module to create a better linear regression line to predict a person's height. You'll need to do two linear regressions and then determine and argue which equation is a "better" model than the other.

TURN IN:

Determine which model is better. Back up your reasoning with the following (and make sure to do the following:

• Use good notation for your regression line equations.
• Use technology to do regression-type calculations and graphs, and include this output in your paper
• Correctly create and include scatter plots, including labels in all the right places (include the plots in what you turn in)
• Correctly create and interpret a residual plot (include the plots in what you turn in)
• Correctly compute and interpret (in a sentence) the correlation coefficients
• Correctly compute and interpret (in a sentence) the coefficients of determination
• Looked for and "dealt with" outliers in a "statistically responsible" manner
• Use the correct response variable
• Sufficiently argue which model is better than the other, citing statistical evidence (i.e. all the stuff above)
• You have done all of the above in two pages or less, typed in paragraph form.