1 Linear Correlation Prepared for SSAC by *David McAvity – The Evergreen State College* © The Washington Center for Improving the Quality of Undergraduate Education. All rights reserved. *2007* Core Quantitative concepts and skills Statistics: Correlation coefficients and linear regression

2 To create a scatter plot you enter your data in two columns, with the first column being the independent variable and the second column being the dependent variable. Select the two columns and then click on the chart wizard. Choose xy (scatter) plot option and select the type without connected lines. Click through the wizard adding chart titles and axis labels – with units when given. Once you have your scatter plot you can find the equation of best fit by a adding a trend line. To add a trend line right click on any data point and choose the add trend line menu option. Choose the linear trend line and then under the options tab check the display equation on chart and display R-squared value on chart options. Scatter Plot Create the scatter plot and regression line using the example below

3 Covariance The correlation coefficient between two variables x and y is a measure of how strongly one variable can be used as a predictor of the second. We calculate the covariance as follows: Where cov(x,y) is the covariance, given by: And var(x) and var(y) are the variances of x and y respectively, given by and In Excel and some other statistics programs the square of the correlation coefficient is quoted instead.

4 Linear Regression The equation for the line of best fit, or the regression line, is given by the equation y=mx+b where and

5 Calculating the Correlation Coefficient and the Regression Line Make sure you understand these formulas by completing the following spreadsheet

6 Lab Assignment 1.Collect the following Data: a)Measure your hand span and height. (Your hand span is the distance from the tip of the thumb to the tip of the pinky when the hand is stretched.). Record these values on the web form on the program webpage. b)Calculate your body mass index (mass in kg divided by the square of your height in meters – look up conversions on the internet). Measure your heart rate at rest, and your heart rate immediately after running around the lecture halls. Find the heart rate ratio: heart rate after exercise/heart rate before exercise. Record your bmi and the heart rate ratio after exercise on the web form on the program webpage 2.Create a spreadsheet and complete the following for each set of data: a)Create a scatter plot. b)Find the mean value of each variable. c)Find the correlation coefficient for each scatter diagram and comment on its value. d)Find the slope and intercept of the equation of the line of best-fit. 3.Post your completed spreadsheet to our program webpage.