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Click to edit Master title style Midterm 3 Wednesday, June 10, 1:10pm.

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Presentation on theme: "Click to edit Master title style Midterm 3 Wednesday, June 10, 1:10pm."— Presentation transcript:

1 Click to edit Master title style Midterm 3 Wednesday, June 10, 1:10pm

2 Click to edit Master title style Research Concepts

3 Click to edit Master title style Regression: Independent and Dependent Variables

4 Click to edit Master title style Regression Instead of deciding whether the independent variable has "some effect" on your dependent variable, we wish to see how well we can predict the dependent variable (response variable) from the independent variable (explanatory variable). Of course, if the independent variable has no effect on the dependent variable, then the independent variable will NOT help us predict the dependent variable. If the independent variable has a strong effect on the dependent variable, then we will be very GOOD at predicting the dependent variable from the independent variable.

5 Click to edit Master title style

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7 Linear (strong correlation) Linear (weak correlation) Linear (strong correlation) Non-linear (strong correlation) Non-linear (strong correlation) Non-linear (no correlation) No Relationship (no correlation)

8 Click to edit Master title style The ‘Coefficient of Correlation’, r How close are the datapoints in the scatterplot to the best-fitting regression line?

9 Click to edit Master title style The Coefficient of Correlation Statistic (r) r is a value between -1 and 1. r = 1: Perfect Positive Linear Correlation r = -1: Perfect Negative Linear Correlation r = 0: No Linear Correlation

10 Click to edit Master title style What Do Correlations Tell Us? Correlations allow us to predict one score from another (using the "regression equation"). Good prediction doesn't always require understanding why there is a relationship. Correlation does not imply causation! Correlations are often due to coincidences or common cause factors.

11 Click to edit Master title style Correlation ≠ Causality r = 0.98

12 Regression Hypotheses Null Hypothesis: Null Hypothesis: H 0 : β 1 = 0 H 0 : β 1 = 0 Alternative Hypothesis: Alternative Hypothesis: H 1 : β 1 ≠ 0 H 1 : β 1 ≠ 0

13 Estimated Parameters From your data, we will get an estimate of β 1. We will call this estimate B 1. From your data, we will get an estimate of β 0. We will call this estimate B 0.

14 Click to edit Master title style Estimated Parameters Slope Intercept (Do not memorize this formula)

15 Click to edit Master title style Predicting Scores B 0 = B 1 =Y = If Mr. Bob's X score is what is his predicted score? What is the deviation score? Y = ^ Y - Y = ^ Intercept Slope


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