Regression

1
Regression

• A/S 305 Social Research Methods
• Sarah Goodrum, Ph.D.

2
Regression

• Simple Linear Regression
• Multiple Regression
• Discrete vs. Continuous Variables
• Dummy Variables
• Tests of Significance and R-squared
• Reporting the Output

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Regression

• is a method of determining the specific function
  relating Y (DV) to X (IV).
• a regression equation provides a mathematical
  description of the relationship b/t the
  variables
• regression is most appropriate with interval,
  ratio, and sometimes ordinal level variables (we
  can get around this by converting nominal level
  variables to dummy variables).

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Simple Linear Regression

• a method of data analysis in which the
  relationship among variables are represented in
  the form of an equation, a regression equation
• involves ONE X (IV) and ONE Y (DV)
• the regression line offers a graphic picture of
  the association between X and Y and
• the regression equation is an efficient way to
  summarize that association.

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Simple Linear Regression Model

• Y a bX
• Y predicted value of the DV
• a value of Y (DV) when X 0
• b the slope of X (IV)
• (aka regression coefficient or beta)
• X the value of the IV
• If we know the values of a (aka the constant)
  and b (aka the coefficient), then we can
  estimate the value of Y for every value of X.

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Simple Linear Regression Model

• Y a bX
• Translation for b
• /-b The coefficient for X (be specific) is
  ___, which means that the effect of X on Y is an
  increase/decrease of ___.
• OR
• b The coefficient of 2.45 for X (be specific)
  indicates that as X increases by one unit, Y
  increases by 2.45.
• -b The coefficient of -4.5 for X indicates that
  as X increases by one unit, Y decreases by 4.5.

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Creating the Model(s)

• To create the equation for Model 1, you take two
  numbers from the Unstandardized Coefficients
  column
• (1) the constant and
• (2) the B value (or slope) for IV1
• the equation will look like
• DV Constant (IV1 x B value for IV1)
• Do not include equation models in final paper.

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Multiple Regression

• a form of statistical analysis that seeks the
  equation representing the impact of two of more
  Xs (IV) on a single Y (DV)
• involves MORE THAN ONE X (IV) and ONE Y (DV)

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Discrete vs. Continuous Variables

• discrete variable variables whose attributes
  form discontinuous chunks (like nominal level
  variables).
• to use discrete variables in regression analyses,
  we convert them to dummy variables
• e.g., gender, race, religious affiliation
• continuous variable variables whose attributes
  form a steady progression
• e.g., age, income

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Dummy Variables

• Since regression is most appropriate with
  interval, ratio, and sometimes ordinal level
  variables
• researchers sometimes transform nominal level
  variables so as to measure the presence or
  absence of ONE of the attributes of the original
  variable.
• GENDER can be transformed/recoded into a measure
  of maleness
• 1male, 0female
• with male respondents being 100 male and female
  respondents being 0 male

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Dummy Variable, Cont.

• RECODING TO CREATE A DUMMY
• Recode the variable SEX so that the recoded -gt
  into different variable values for the dummy
  variable for MALE will be
• 1 -gt 1 . . . 100 majority group status/male
• 2 -gt 0 . . . 0 minority group status/not male
• system missing -gt system missing
• user/system missing -gt system missing

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Multiple Regression Model

• Y a b1X1 b2X2 b3X3
• Y predicted value of the DV
• a value of Y (DV) when X 0
• b1 the slope of X1 (IV)
• X1 the actual value of IV1
• b2 the slope of X2 (IV)
• X2 the actual value of IV2
• b3 the slope of X3 (IV)
• X3 the actual value of IV3

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Multiple Regression Model

• Y a b1X1 b2X2 b3X3
• Translation for b1 when continuous
• The coefficient for X1 (be specific) is ___,
  which means that the effect of X on Y is an
  increase/decrease of ___, controlling for X2 and
  X3 (be specific).
• OR
• The coefficient of 2.45 for X1 (be specific)
  indicates that as X1 increases by one unit, Y
  increases by 2.45, controlling for X2 and X3.
• The coefficient of -4.5 for X1 indicates that as
  X1 increases by one unit, Y decreases by 4.5,
  controlling for X2 and X3.

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Multiple Regression Model

• Y a b1X1 b2X2 b3X3
• Translation for b1 when discrete
• The coefficient for X1 (be specific) is ___,
  which means that the effect of being X11 on Y
  is an increase/decrease of ___, controlling for
  X2 and X3 (be specific).

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Tests of Significance and R2

• t-test (for variable) indicates if the effect
  of X on Y is significant.
• SPSS will give you the p-value for each X want
  plt0.05
• t26.10 and p0.00 for X1 in Model 1 can be
  reported as
• The effect of X1 (be specific) on Y is
  significant.
• also, we report significance in the TABLE OUTPUT
  with a for the relevant coefficient, which
  means plt0.05 as noted in a table footnote
• coefficients with no are assumed to not be
  significant
• F-test (for model) tests overall significance
  of the model when using more than one X.
• SPSS will give the p-value for the F-test want p
  lt 0.05
• F-value of 56.5 and p0.02 should be reported as
• F-value of 56.5 and p-value of 0.02 indicates
  that Model 1 is significant in predicting Y (DV)
  (be specific).

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Tests of Significance and R2

• R-squared (for model) indicates the amount of
  variance in the dependent variable explained by
  the independent variable(s) in the model
• SPSS will give you the R-squared for each Model
• R2 0.123 can be reported as
• The R2 is 0.123 which suggests that 12 of the
  variance in Y (be specific) is explained by X1,
  X2, and X3.

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Reporting the Output

• WHAT SPSS OUTPUT TO READ
• Focus on the
• Coefficients Table (B and p-value)
• ANOVA Table (F-test and p-value)
• Model Summary Table (R2)
• In stepwise regression, SPSS begins by creating
  the most effective model equation possible with
  only one IV
• i.e., if you had to measure your DV using only
  one IV, SPSS tells you that youd do best with
  the IV listed in the FIRST model

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Reporting the Output

• WHAT TO SAY ABOUT THE OUTPUT
• Coefficients Table
• Model 1 b and p-value for each IV
• ANOVA Table
• Model 1 F-test and p-value
• Model Summary
• Model 1 R-squared
• Repeat above for Model 2
• Report output one Model at-a-time.