# Statistical Analysis Regression - Correlation - PowerPoint PPT Presentation

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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.

### 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.

### 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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