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Statistical Analysis Regression - Correlation

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Statistical AnalysisRegression - Correlation

Roderick Graham

Fashion Institute of Technology

- Earlier in the semester we looked at one measure (Ex: height, a scale for video game usage) and compared the mean of that measure to a sample. These were univariate analyses.
- In this chapter we will now look at how two different measures may influence, or “relate” to one another.
- We call these types of analyses bivariate (two variables)
- We will be looking for possible correlations (co-relation) between two measurements.

- Question: For our previous work, how did we (you) visually summarize data?
- Histograms
- Frequency Polygons (Line Graphs)
- Pie Graphs (Circle Graphs)

- Now, when we are trying to compare variables, we use a different summary technique:
- a scatter plot.

- Let’s say we wanted to look at the relationship between IQ and Income. We believe that the smarter someone is, the more money they make.
- Let’s say we have this survey question: What is your income over the last year before taxes?
- Next we give each respondent an IQ test and recorded the results.
- And then, we plot the points.

What’s up with this guy?

Can we suggest that there is a relationship between income and IQ?

Y – Axis for “Effect” Variable

X – Axis for “Cause” Variable

- Another way of saying that there is a relationship between two variables is to say they are correlated
- Correlation is the ability of one variable to predict the value of another variable
- For our IQ and income example, we can say that there is a correlation between IQ and Income

- Later we will discuss how we measure this relationship mathematically. But first there is more to our scatter plot story….

“Regression Line” Summarizes Relationship between X and Y

Because the line slowly rises, you can say that this is a positive relationship.

The closer the dots cluster around this line, the stronger the relationship between X and Y

The steeper the rise, the stronger is the relationship (X affects Y more)

- The regression line summarizes the relationship between two variables.
- We can always do this line by hand to summarize the relationship
- But there is a formula that we will use that allows us to pick the “best fitting” line. We will learn this formula.

- The types of analyses you will be doing require that the relationship between two variables be linear: You have to be able to summarize a relationship between X and Y with a regression line.

Can we suggest that IQ causes an increase in income?

NO! Correlation never means causation!

We think that the number of children in a home influences the hours per week a husband spends on housework. Thus Number of Children = X and Hours Per Week = Y

- You will be asked to plot things by hand in this class
- Do not worry so much about “neatness” – graphing paper is not necessary
- Sometimes I will give you the units upon which to start your axes, and the units on the axes.
- Sometimes no.

- Conceptually, we are now moving into measuring relationships between two different variables. We are looking at bivariate data. We are looking for possible correlations between two measures.
- Before we begin our analyses, we get a visual description of the relationship using a scatterplot.
- The variable we think is causing the influence is on the X (horizontal) axis and the variable we think is being effected is on the Y (vertical) axis.

END