Posted: April 6th, 2016

# Regression slope: Is there a slope? Has its significance been explained? Has the slope of the equation been explained, that is, for each unit increase in the x-variable, by how much does the y-variable change?

1. Introduction: What is it that the student is trying to find out? Why? To whom would the
information be useful? Is this well stated and easily understood from what the
student has written? 10 pts.
2. Sources: Has the student fully cited the sources of his data? Is the source authoritative? If the student refers to a popular controversy or other issue, does the student cite sources concerning this dispute? 10 pts.
3. Data Adequacy: Is the data suitable to answer the hypothesis question? (For instance, when two ratios are the proper data, some students have mixed quantities with ratios. One, for example, used the number of crimes committed in states versus the number of people unemployed in states. Surely the bigger states would have more crimes and more people unemployed independent of any relationship between these two variables. What should have been done was that the student should have taken rates of unemployment and rates of crime. This makes the standard of measurement equivalent across states of various populations.) Is the data cross sectional? Is it the most recent data, particularly if it’s sports data? At least 30 paired observations? 10 pts.
4. Are the independent and dependent variables properly identified (that is, not confused)? 10 pts
5. Regression hypothesis: 40 pts
a. Is this correctly and clearly stated? (Students have often confused the null hypothesis for the alternative hypothesis.) (10 pts.)
b. Is the decision criterion clearly stated, that is, is the alpha given? (10 pts.)
c. Is the critical value for the F-test or t-test accurately given? (10 pts.)
d. Does the student state the expected sign on the slope coefficient? (10 pts.)
6. P-value: What is it? Is it clearly mentioned and explained? 10 pts.
7. Regression slope: Is there a slope? Has its significance been explained? Has the slope of the equation been explained, that is, for each unit increase in the x-variable, by how much does the y-variable change? Is this clearly and correctly interpreted? 10 pts.
8. Coefficient of determination (or correlation coefficient): Is the coefficient of determination given? Is it accurately and clearly interpreted? This means does the student state its relative strength? Furthermore, does the student accurately interpret it by answering the question, “what is the percentage of the variation in the y-variable that can be explained by variation in the x-variable?” 10 pts.
9. Residuals: What do they suggest? Do they suggest that the regression assumptions are upheld? Or do the suggest heteroscedasticity? Or do they suggest that a higher order equation, that is a non-linear equation, is more appropriate? Why? 10 pts.
10. Has the student checked for outliers? 10 pts.
11. Conclusion: Does the student draw out the implications of the findings? Does the student adequately criticize her or his results? Does the student make suggestions about how the study could be improved or does the student mention the study’s limitations? 10 pts.
12. Writing style: Does the student keep writing errors, both in style and grammar, to a minimum? The student’s writing should be clear, concise, and grammatically correct. Citations and information sources should be correctly footnoted or embedded. 10 pts.
13. Does the student include the appropriate output: ANOVA table, residuals, residual plot, and line fit plot? Is the line shown (i.e., the dots connected)? 10 pts.

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