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Multiple Regression II Fenster

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Multiple Regression Let’s go through an example using multiple regression and compare results between simple regression and multiple regression.

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Teacher Salary Hypothesis Let’s say one hypothesized that: H 1 : The higher the teacher salary in a county, the better students performed on state mandated assessments.

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Teacher Salary Hypothesis The researcher was interested in studying the relationship between teacher salary and student performance on state mandated assessments at the county level. Unit of analysis is county. Since the researcher lives in FL, she chose to collect data on that state.

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Teacher Salary Hypothesis So there are 67 counties in FL. DSSMATH is a state mandated assessment that can be used to measure yearly progress in math for the NCLB act. DSSREA is a state mandated assessment that can be used to measure yearly progress in reading for the NCLB act.

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Univariate Analysis

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I would conclude that all of my variables are at least “reasonably” normally distributed.

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Pearson Product Moment Correlations on the data Did we find support for H 1 ?

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Spearman’s rho correlations on the data

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Regression and Pearson correlations essentially the same test We can get the same result in simple regression that we got with the Pearson Product Moment correlation (assuming we use the same set of data).

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Results for simple regression: Math

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The “sig” we see on the SPSS results page represents a two-tailed probability value. We should divide that probability value in ½ to give us a one-tailed probablity.

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Results for simple regression: Math Can we reject the null hypothesis for H 1 ? What probability value did we get for the relationship between teacher salary and DSS MATH when using correlation? Answer.018 What probability value did we get for the relationship between teacher salary and DSS MATH when using correlation regression? Answer.037/2=.018

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Results for simple regression: Math

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Simple Regression Results for Reading

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Can we reject the null hypothesis for H 1 when it comes to reading? What probability value did we get for the relationship between teacher salary and DSS REA when using correlation? Answer.106 What probability value did we get for the relationship between teacher salary and DSS REA when using correlation regression? Answer.213/2=.106 WE FAIL TO REJECT THE NULL FOR READING!

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Multiple Regression Results for Reading

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What did we find with respect to H 1 in the multivariate case? Do we find support for the hypothesis that the higher the teacher salary, the better a county scored on state mandated assessment? Answer: NO! We find a very slight relationship the other way, the higher the teacher salary the LOWER a county scored on state mandated assessment.

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Multiple Regression Results for Reading We DO find a VERY strong statistical relationship between the percentage of students in a county on free and reduced lunch and scores on state mandated assessments. What would we conclude? At the bivariate level, with no statistical controls, we found no relationship between teacher salary and reading performance.

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Multiple Regression Results for Reading At the multivariate level, controlling for the percentage of students on free and reduced lunch, we still find no effect.

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Multiple Regression Results for Reading

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Multiple Regression Results for Math

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What did we find with respect to the H 1 in the multivariate case for math? Do we find support at the multivariate level for the hypothesis that the higher the teacher salary, the better a county scored on state mandated assessment? Answer: NO! We find a very slight positive relationship, but the effect is not close to what we need to claim “statistical significance”.

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Multiple Regression Results for Math

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