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Simple Bivariate Regression
PSGE 7211
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Most widely used statistical technique in the social sciences
What is Regression? (Multiple) regression is a statistical method for studying the relationship between a single dependent variable and one or more independent variables Most widely used statistical technique in the social sciences
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Clarification of Terms
Dependent Variable (DV) Response, Outcome Independent Variable (IV) Predictor, Explanatory, Regressor, Covariate
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What is Regression good for?
Prediction: you can combine many variables to produce optimal predictions of the dependent variable Causal Analysis: it separates the effects of independent variables on the dependent variable so you can isolate the unique contribution of each variable
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The Power of Regression
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Predict and Explain Understanding the causes of poor academic performance will allow us to predict who will have trouble in school Motivational beliefs Goals, Task value, Interest Anxiety
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Variables in Regression Analysis
You can use... Nominal Interval Ratio/Continuous Categorical Continuous
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Why is regression linear?
Regression analysis is also known as linear regression because it is based on a linear equation (y = a + bx) If you graph a linear equation, you get a ...
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Why is Regression linear?
A straight line!
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INCOME = 8,000 + (1,000 x SCHOOLING)
An example DV = person’s annual income IV = number of years of schooling completed Regress INCOME on number of years of schooling completed INCOME = 8,000 + (1,000 x SCHOOLING)
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INCOME = 8,000 + (1,000 x SCHOOLING)
Income & Schooling INCOME = 8,000 + (1,000 x SCHOOLING) Years of Schooling Income 1 2 3 4 5 6 7 8,000 + (1,000 x 0) = 8,000 8,000 + (1,000 x 1) = 9,000 8,000 + (1,000 x 2) = 10,000 8,000 + (1,000 x 3) = 11,000 8,000 + (1,000 x 4) = 12,000 8,000 + (1,000 x 5) = 13,000 8,000 + (1,000 x 6) = 14,000 8,000 + (1,000 x 7) = 15,000
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Income & Schooling EXPLAIN: How would you explain the relation between income and schooling? PREDICT: If a person has 10 years of schooling, what would be his/her income?
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INCOME y DV = 8,000 a intercept + 1,000 b slope (SCHOOLING) x
Linear Equation INCOME y DV = 8,000 a intercept + 1,000 b slope (SCHOOLING) x (variable x) Point on the vertical axis which “intercepts” the line or the value of y when x is 0. The amount of change in y we get for every 1-unit change in x The larger the slope, the steeper the line!
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Income & Schooling y Slope Intercept x = # years schooling
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IV = # hours per week on math homework
Another example DV = Math Achievement IV = # hours per week on math homework Regress math achievement on number of hours spent per week on math homework ACHV’T = a + b(HW)
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Achievement & Homework
Step 1 – Look at descriptives
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Achievement & Homework
Step 2 – Look at correlations
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Achievement & Homework
Math Achv’t For bivariate regressions, the R is equivalent to correlation coefficient (Pearson’s R) The R-Square coefficient denotes the variance explained in the outcome variable by the predictor variable; Homework explains .102 or 10.2% of the variance in math achv’t HW .102
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Is the model significant?
Variance explained Variance unexplained Look at the F-Statistic. Is it significant? What does this mean? Null hypothesis for Regression: Slope of the regression line = 0 (or no relation)
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y’ = a + bx + e The Regression Equation
Predicted value of math achv’t = (# of homework hours) Note that the statistic is also significant as determined by the following formula:
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Regression Line
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b = unstandardized coefficients
b and Betas b = unstandardized coefficients β= standardized coefficients (b transformed into standard deviation units)
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Interpreting Regression output
In order to examine what effect X had on Y, I regressed the DV on the IV Results suggest that the overall model [was/was not] statistically significant, F (1, 98)=11.18, p=.001 The R-squared was .10, indicating that… X [was/was not] statistically significant predictor of Y
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In pairs, discuss the output – how would you interpret the output?
Lab Time In pairs, discuss the output – how would you interpret the output? Discuss what bivariate regression analysis you will run Confirm that you understand the steps for running SPSS
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SPSS – Bivariate Regression
STEP 1
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SPSS – Bivariate Regression
STEP 2
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SPSS – Bivariate Regression
STEP 3
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SPSS – Bivariate Regression
STEP 3
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Exit Ticket Interpret the output
What does this analysis do? What should you report when you write up a regression analysis? If you want, go to 1025 and run your HW 4 output.
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