POLS-3328 Fall 2010-- Lecture Outline

November 9, 2010

Readings:

Chapter 12 Bivariate Data Analysis (Johnson and Reynolds) (pp 477-490, 490-498) 
Chapter 8 Correlation and Linear Regression (Pollock) (pp. 170-173)

COURSE LEARNING OBJECTIVES

  1. Students will learn the research methods commonly used in behavioral sciences and will be able to interpret and explain empirical data.

  2. Students will achieve competency in conducting statistical data analysis using the SPSS software program

 

Bivariate Regression

Lets Try a correlation from a 1990's State of America's Cities

 

Bivariate Regression

Bivariate linear regression is an important statistical technique in Political Science.  It allows us to measure the effects of an independent variable on a dependent variable. Conducting this in SPSS is simple, but understanding can be difficult.

When you can use regression

  1. If you have a ratio dependent variable that takes on at least 11 values
  2. You need ratio level independent variables (some argue that you can use ordinals, but be careful)
  3. If you have 30 or more cases (N>30)
  4. If you have a linear relationship. It will not work with curvilinear or exponential relationships.

 

Back to Scatterplots and how they Relate to Regression

The Dataset, and use the previous lecture notes to create a scatterplot

Y= Grade on Final Exam
X= Average Grade on First and Second Exams

What the Line is all about

  1. The Line of Best Fit- it is the line that best describes the data.  It shows us the direction of the relationship



  2. How much error is in our line- the farther the dots are away from the line, the more error in our prediction.  If all the dots were on the line we would have a perfect relationship. 



  3. A predictor for future values

 

In Bivariate regression, our model is

Y= a + b(X) +e

The Concept of Linear Regression is based on the slope-intercept model of Algebra

Where

Y=  the value of the dependent variable.  It can also be the predicted score

a(lpha)=  the constant, or the point at which the line crosses the y-axis.. 

X= the value of our independent variable.  This is the score being used as the predictor. 

b(eta)=  the slope and direction of the line

e=  The error term,  what is missing from your regression.  

Here is the information from the Example above  (using the non-legacy scatterplot function). 

Y= Final Exam 

a=  16.24 the constant  (the value in where our line crosses the y-axis)

b=   .780  (the slope of the line).  It is positive, so that as the score on the early exams goes up, the score on the final exam goes up.  It also means that every point the early exams increase, the final exams increase .780 points!

X (examavg)=  oh, lets say a grade of  80 from the example above

Pop it into the formula

Y= a +b(x)

Y = 16.24 +.780(80)

Y=16.24 + 62.4

Y= 78.64

So the Predicted value of Y  also called (Y prime) would be 78.64 if the student averaged an 80 on the first and second exams!

 

TO COMPUTE A BIVARIATE REGRESSION MODEL IN SPSS

Lets try out another dataset

You must have a ratio-level dependent variable

  1. Analyze
  2. Regression
  3. Linear

You place your dependent and independent variables in the appropriate places and select ok.

READING THE OUTPUTS
Regression Outputs are very simple to understand.
 

Constant-  this says the value of the dependent variable, if the independent variable is zero.

INDEPENDENT VARIABLES- (in this case Vehicle Weight)- This is our independent variable. 

For Every lb a car weighs,  fuel efficiency decreases by .008 miles per gallon!

T-Statistic= computed by dividing the beta coefficient by the standard error.   

 

Lets Try an Example

Null Hypothesis-  There is no relationship between a state's Union population and the per capita income

Y=
Constant =
Beta and direction= 


Is this significant and why?

What would the predicted per capita income be for a state with a union % of 25?

 

Lets look at some examples about Health Care

Minority Population and Access to Health Care

For Each Example, What is the

  1. Alpha Value- what does it mean

  2. beta value

    • direction

    • size- what does it mean

  3. Significance of Relationship and Why

  4. Strength of Relationship (standardized beta coefficient)

  5. Practical Significance

Median Family Income and Health Insurance

For Each Example, What is the

  1. Alpha Value- what does it mean

  2. beta value

    • direction

    • size- what does it mean

  3. Significance of Relationship and Why

  4. Strength of Relationship (standardized beta coefficient)

  5. Practical Significance

 

WHAT ABOUT HERE?:  The influence of female legislators or global defense spending?

  1. What is the Constant?

  2. Is our independent variable significant, why or why not?

  3. Is it a positive or negative relationship?

  4. How much change in the military budget results from a change in 1% of parliamentary seats held by females.

  5. What is the potential practical significance of this?

 


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