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Linear Regression - Political Science - Lecture Slides, Slides of Political Science

Bharat Ratna Dr. B. R. Ambedkar UniversityPolitical Science

Linear Regression, Looking at a Scatterplot, Fitting a Regression Line, Reputation, Confound, Independent Variables, Graduation Rates, Scores and Graduation Rates, Relationship, Regression Line are some points of this lecture.

Typology: Slides

2011/2012

Uploaded on 12/31/2012

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Linear Regression I:
Scatterplots and Regression Lines
•SAT scores and graduation rates
–Looking at a scatterplot
–Fitting a regression line
–What does it mean?
•Other factors that affect graduation rates
–Confound: reputation
–Other independent variables
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Linear Regression I:

Scatterplots and Regression Lines

  • SAT scores and graduation rates
    • Looking at a scatterplot
    • Fitting a regression line
    • What does it mean?
  • Other factors that affect graduation rates
    • Confound: reputation
    • Other independent variables

SAT Scores and Graduation Rates

  • To test the hypothesis that colleges with smarter students have higher graduation rates, I will look at data from 148 colleges in the United States.

SAT Scores Graduation Rates

SAT Scores and Graduation Rates

  • We can summarize the direction and strength of a relationship between two variables by calculating “r,” the correlation. (Pollock, p. 171-174)
  • If we want to know more about the relationship, we can fit a “regression line” to the scatterplot.

SAT Scores and Graduation Rates

Average SAT Score

Graduation Rate 600 800 1000 1200 1400 1600

100

80

60

40

20 0 Rsq = 0.

SAT Scores and Graduation Rates

  • Like all lines, a regression line can be summarized with this formula:

y = a + b•x

where: b = slope of line or “regression coefficient” a = the intercept, or the value of y when x=

SAT Scores and Graduation Rates

  • The regression coefficient for the effect of SAT scores on graduation rates is 0.06. - This is the predicted effect on graduation rates when SAT scores go up by one unit. - This means that comparing one college to another college where average SATs were 100 points higher should lead to a graduation rate that is 6 percentage points higher.

Other Factors Affecting Grad Rates

Student/faculty ratio

Graduation Rate 0 10 20 30

100 80 60 40 20 0 Rsq = 0. In-state Tuition

Graduation Rate 0 2000 4000 6000 8000 10000 12000 14000

100 80 60 40 20 0 Rsq = 0.

Other Factors Affecting Grad Rates

Year of

Founding

SAT Scores Graduation Tuition Rates

Student/Faculty Ratio