# Linear Regression on Leg Length and Lunge Length

1. I need to analyze the data in Worksheet 5-5 (attached). This data is real data that was collected by a doctor who specialized in leg and knee injuries. He gathered data from 43 people, indicated by their initials. Each person was required to perform three anterior (frontward) lunges with the right leg followed by three with the left leg. The distances were recorded. The person was then required to do three lateral (sideways) lunges with the right leg followed by three with the left leg. To use these lunges you will need to average the three trials to get a mean. You can use the Excel "=average(cellsReferenced)" computation to do this. By copying the formula down the column the task you can make short work of this. Not all of the tests below use the lunge information.

2. Complete a correlation and regression analysis on the data.

3. Answer the following questions:

a. Is there a difference in leg length (right v. left)? Use a paired t-test to determine the answer. Show all steps.

b. Is there a difference in lateral lunge (right v. left)? Use paired t-test to determine the answer. Show all steps.

c. Is there a correlation of height and leg length?

d. Is it possible to predict anterior lunge scores if the length of a patient's leg is known? Is it possible to predict anterior lunge scores if his/her height is known? Which is the better predictor? Show the scatter diagram with the linear regression equation for the best predictor.

#### Solution Preview

1. I need to analyze the data in Worksheet 5-5. This data is real data that was collected by a doctor who specialized in leg and knee injuries. He gathered data from 43 people, indicated by their initials. Each person was required to perform three anterior (frontward) lunges with the right leg followed by three with the left leg. The distances were recorded. The person was then required to do three lateral (sideways) lunges with the right leg followed by three with the left leg.

To use these lunges you will need to average the three trials to get a mean. You can use the Excel "=average(cellsReferenced)" computation to do this. By copying the formula down the column the task you can make short work of this. Not all of the tests below use the lunge information.

I calculated the average lunge for each person in the Excel worksheet.

2. Complete a correlation and regression analysis on the data.

I did these analyses in SPSS, just because I think it's easier to do a regression analysis using that software rather than Excel. If you prefer using Excel, you should still get the same results.

I only used the data in the second Excel worksheet (the means we calculated in part 1).

Correlation analysis:

(1) First, I looked at the correlations between each of the variables except for gender (using Pearson's correlation coefficient). There are several statistically significant correlations:

height and ...

#### Solution Summary

A correlation analysis and a regression analysis were performed on a set of data (found in the attached Excel spreadsheet). These analyses, as well as additional t-tests, were used to answer questions about the data (questions 3a - 3d).