Simple Regression:
The Teacher Preparation Research Team conducted a study of college students who took the Praxis II-a teacher certification examination. Some variables from their data set include:
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Variable
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Description
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id
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Participant ID.
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Observe (one unit = one hour/week)
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Number of hours/week spent observing elementary school classrooms.
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prax2ec (one unit = one point on the exam)
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Score on the early childhood content knowledge portion of the Praxis II exam.
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The researchers predict that number of hours/week spent observing elementary school classrooms will be positively associated with students' performance on the Praxis II.
Part I: Using the Praxis data set, please answer the questions below:
1. What is the correlation between prax2ec and observe? Describe the nature of this correlation. Show how the correlation can be computed using the covariance between these two variables and their standard deviations.
2. Regress prax2ec onto observe. How much of the variance in prax2ec is accounted for by observe? Show how r-square may be determined using the correlation between prax2ec and observe. Show how r-square may be determined using information presented in the ANOVA table.
3. Locate and interpret the standard error of estimation. Show how this value is calculated using values presented in the ANOVA table.
4. What is meant by the term, "residual?"
5. Explain how the degrees of freedom for the residual term was calculated for this model.
6. Calculate the slope and the intercept for this regression equation. Show your work (and refer me to where I can find these calculations in your Stata printout).
7. Write out the regression equation. Interpret the meaning of the slope in this equation. Interpret the intercept.
8. Examine participant #42. Using the regression equation, what would you predict this individual's Praxis II exam score to be? Did your regression equation over- or under- predict this person's actual score?
9. Plot your regression line in a figure. This figure should be in APA style.
10. Think about the limitations to the development and use of your model. What predictors might you add to this model to account for additional variance in students' Praxis II exam scores?
Part II: Provide a brief write-up of your regression results.
Example write-up (use the same format as you do your homework)
We hypothesized that educational attainment would be associated with political knowledge scores. To test this hypothesis, we conducted a simple linear regression estimating political knowledge from the highest grade completed. The results support this prediction. Students with more education display more political knowledge, b = 0.972, t(341) = 9.504, p < .001. Specifically, for two students who differ by one year in their highest grade completed, the student who completed the additional year of schooling is expected to have a political knowledge score that is approximately one point higher than the student with one less year of schooling. Students' educational attainment accounted for 35% of the variation in their political knowledge scores, r2 = .3512.