Descriptive Statistics: Correlation Descriptive Statistics: Correlation Describes the relationship between two or more variables. Describes the strength of the relationship in terms of a number from -1.0 to +1.0. Describes the direction of the relationship as positive or negative.
26
Embed
Descriptive Statistics: Correlation u Describes the relationship between two or more variables. u Describes the strength of the relationship in terms of.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
IQ and reading achievement Anxiety and test scores Amount of calories consumed and weight gain. Amount of exercise and weight gain Reading achievement and math achievement Foot size and math ability
Caution!Caution!
Correlation does not indicate causation. Correlation only establishes that a relationship
exists; it reflects the amount of variability that is shared between two variables and what they have in common.
Examples: Amount of ice sold and number of bee stings. SAT scores and GPA in college.
A Picture of CorrelationA Picture of Correlation
A scatter plot visually represents a correlation The X axis is on the horizontal
The variable on the x-axis is called the explanatory, or predictor variable.
The Y axis is on the vertical. The variable on the y axis is called the response
Higher correlations are expected in a heterogeneous population than in a homogeneous one. Example: In elementary and high school, there
is a positive correlation between height and success in basketball.
Example: In the pros, there is no such correlation.
Conditions to CheckConditions to Check
Quantitative Variable Condition: correlation only applies to quantitative variables. Make sure you know what your units are, and what they measure.
Straight Enough Condition: correlation only applies to linear relationships.
Outlier Condition: some outliers can alter correlation greatly. Be sure to check correlation with the point, and again without the point.
Formula for CorrelationFormula for Correlation
Creating Scatterplots on the Creating Scatterplots on the CASCAS
You will first need a data set. From the home screen of the CAS, go to NEW DOCUMENT (enter), ADD LIST & SPREADSHEETS (enter).
Go to the top of Column A, and name your data. For now, use “HP” for our data Horsepower. Go to cell A1, and start entering the data: 200, 230, 200, 148, 291, 300, 295
Creating Scatterplots on the Creating Scatterplots on the CASCAS
Now, go to the top of Column B, and name this column “MPG” for our data Highway Gas Mileage.
Go to cell B1 and begin entering data: 32, 30, 30, 32, 22, 20, 21
Next, press “CTRL” “I” “ADD DATA & STATISTICS”
Move your cursor down to the x axis.
Creating Scatterplots on the Creating Scatterplots on the CASCAS
You should see the outline of a small box, and the text “click to add a variable”.
Click inside the box and add “HP” Do the same for the y axis, “click to add a
variable”, add “MPG”. You now have a scatterplot.
Practice:Practice:
Describe the association of the scatterplot on your CAS.
More Goodies on the CASMore Goodies on the CAS
You can also find the correlation coefficient on your CAS. Follow the steps on the next slide to do so.
Finding the Correlation Finding the Correlation Coefficient on the CASCoefficient on the CAS
Go back to your spreadsheet (shortcut: press CTRL and the left arrow key of the center NAV PAD of the CAS)
Press MENU, STATISTICS, STAT CALCS, LINEAR REGRESSION ( a + bx) …… or Menu, 4, 1, 4
A box will pop open. Only do the following:
XLIST: choose the column you entered the x variable,
(make sure that “a[]” is in this box)
YLIST: choose the column you entered the y variable,
(for this example, “b[]” )
Finding the Correlation Finding the Correlation Coefficient on the CASCoefficient on the CAS
Tab all the way down to the last box that reads “1st Result Column”. This is where you tell the CAS the column you would like the results in. Choose anything but “a[]”, and “b[]”. I usually put the results in “c[]”.
Press enter, and you will see many things fill column C
Finding the Correlation Finding the Correlation Coefficient on the CASCoefficient on the CAS
Now, you try one by yourselfNow, you try one by yourself
Find the correlation coefficient for the following data on several fast food burgers: