MATH 1107 Elementary Statistics Lecture 6 Scatterplots, Association and Correlation

Take a look at the data on the right. In the US, Is there a relationship between: –Household income and violent crime? –Household income and Death rate? If there is a relationship, is it direct or inverse? If there is a significant relationship, can we use it to predict the likelihood of crime or death rate in a particular state? MATH 1107 – Scatterplot, Association and Correlation

MATH 1107 – Scatterplot, Association and Correlation Using scatterplots, we can evaluate the direction, the form, and the strength of the relationship:

MATH 1107 – Scatterplot, Association and Correlation Evaluate the direction, the form, and the strength of the relationship:

Specifically, here are the things to look for in a scatterplot: 1. Direction – Does the direction of the data move NW to SE? This indicates a negative relationship. Does the data move from the SW to the NE? This is a positive relationship. Does the data look like a cloud? This indicates no relationship. 2.Form – Does the data demonstrate a linear pattern? A curved pattern? 3. Strength – Is the data really tight? This indicates a strong correlation. Is the data really spreadout? This indicates a weak correlation. 4. Are there any outliers? Or groups of outliers? MATH 1107 – Scatterplot, Association and Correlation

A few additional points about scatterplots: 1.The dependent variable – typically the one that you want to better understand or predict – is plotted on the y-axis and the independent variable is plotted on the x- axis. 2.We typically only use scatterplots with quantitative data. Question – why? 3.Rescale the scatterplot to only include the scales necessary to see the relationships. However, if the axes do not start at zero, this should be noted at the bottom of the page. Question – why? 4.Changing the units of a scatterplot should not change the relationship (i.e., lbs to kg) MATH 1107 – Scatterplot, Association and Correlation

Correlations can be measured as a number between 0 and 1 (absolute value). Where, numbers closer to 0 indicate less correlation and numbers closer to 1 indicate more correlation. A basic interpretation of the correlation coefficient is – x% of the change in variables 1 and two move together. Correlation coefficients are really not expressed in meaningful units. And…remember that correlation coefficients are related to LINEAR relationships! MATH 1107 – Scatterplot, Association and Correlation

Lets examine some scatterplots and correlation coefficients in EXCEL. Go to the EXCEL datasets on the website. MATH 1107 – Scatterplot, Association and Correlation