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Regression vs. correlation?
Correlation is used to test whether two variables covary, the strength of the relationship, and the direction of the association. A correlation calculation will generate a P-value and a correlation coefficient (r). By comparison, regression will generate the slope and intercept for a best-fit line that can be used to predict unknown values for the dependent variable.
What percentage of depression is not associated with Facebook usage?
The coefficient of determination (r2) is 0.661, which means that 66.1% of the variance in depression is due to the amount of time spent on Facebook; therefore, 33.9% of the variation in depression cannot be explained by time spent on Facebook.
Q3: Variables that could be contributing to the variance not explained by time spent on Facebook?
The unexplained variance in depression scores is the amount of error between measured levels of depression for a study subject and what was predicted by the regression line. This error is due to other variables, possibly naturally-occurring variation. Natural variation in depression could be explained in part by genetic differences or environmental factors like early life experiences (Klengel & Binder, 2013). The amount of variation explained by genetic factors is represented by the standard error of estimate, but the magnitude of the contribution, if it exists, is unknown.
Q4: Confident in the predictive power of the regression equation?
Yes, the significance of the correlation suggests that the chances of making a prediction error are less than 1 in 1000 (p < 0.000). Stated another way, the amount of time spent on Facebook would correctly predict...
This relationship is positive, which suggests that more time on Facebook is associated with higher levels of depression. What cannot be determined is whether there is a causal relationship, since time on Facebook could be contributing to depression or vice versa, or the relationship could be indirect. The only conclusion that can be drawn is that time on Facebook is a good predictor of depression.
Q6: Calculate depression score based on 120 minutes per week Facebook time.
From the table of coefficients the slope of the regression line is 0.135 and the intercept is 3.061. The depression score predicted by 120 minutes of Facebook time is therefore 3.061 + 0.135*120 = 19.261. A quick comparison with the group means reveals this answer is probably correct.
Assignment 2.2: One-Way ANOVA
Q1: Complete the table:
Groups: Drug administration daily, weekly, or null
12 rats per group
Outcome measure is the number of food pellets consumed per month
Source
SS
df
MS
F
Between Groups (Treatment)
24
2
12
6
Within Groups (Error)
66
33
2
Total
78
35
Q2: Find the critical F. value for an alpha of 0.05.
Fcrit (2, 33) = 3.285 for the above data.
Q3: Evaluate the above findings.
The Fcrit (2, 33) value of 3.285 is significantly below the F. value of 6, therefore, the results are significant using an alpha of 0.05. This result forces us to reject the null hypothesis for this experiment, which would be…
References
Klengel, T. & Binder E.B. (2013). Gene-environment interactions in major depressive disorder. Canadian Journal of Psychiatry, 58(2), 76-83.
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Correlation and Regression The ability to evaluate the essential general assumptions underlying statistical models and to distinguish the concepts and techniques of regression analysis is important for scholarly research. This is a more important element for a doctoral learner focused on quantitative research in order to generate appropriate and credible conclusions. Interpreting types of variables, design frameworks, and treatments in statistical regression analysis is also an essential skill for upcoming research
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