Statistical analysis regression correlation
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Statistical Analysis Regression - Correlation. Roderick Graham Fashion Institute of Technology. Conceptual Background.

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Statistical Analysis Regression - Correlation

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Statistical AnalysisRegression - Correlation

Roderick Graham

Fashion Institute of Technology

Conceptual Background

  • 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.

Conceptual Background

  • 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.

Conceptual Background

  • 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.

Conceptual BackgroundEx: Looking at the relationship between income and IQ

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

Conceptual BackgroundEx: Looking at the relationship between income and IQ

  • 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….

Conceptual BackgroundEx: Looking at the relationship between income and IQ

“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)

Conceptual Background

  • 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.

Conceptual Background: Different types of correlations

Correlation and Causation

Can we suggest that IQ causes an increase in income?

NO! Correlation never means causation!

Moving from Data to Plotting

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

Moving from Data to Plotting

  • 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.

Practicing Plotting – Do this problem at your desks/stations!

Your plot should look something like this…

The regression line for this data (using SPSS), looks like this…

Practicing Plotting – Do this problem at your desks/stations

Practicing Plotting – A Perfect Non-Linear Relationship!

Let’s Review

  • 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.


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