Regression
IV, DV, and Variable Scale
t-test
Multiple regression
100
Money' = 200 + 3.75 years
State the predictor variable and the outcome variable
Predictor = years
Outcome = game score
100
Write out the unstandardized regression equation for professor effectiveness
Effectiveness = 0.69 rapport + 0.34 autonomy support + e
100
What is the effect size for t-tests? Please explain it.
Cohen's D, aka standardized mean difference, is the effect size for t-tests. Essentially compares mean difference to variability.
Introduced by Jacob Cohen, an American psychologist and statistician who worked during the 1960s and after.
100
True or false: before conducting multiple regression, you need to make sure relations between predictor variables and outcome variable are linear and strong.
True
200
Complete this sentence: as the amount of years goes buy, money goes up. So, the direction of the correlation between these variables (goes up/down and is positive/negative)
Goes up and positive
200
Write out the unstandardized regression equation for classes missed
Classes missed = -0.54 rapport + 0.02 autonomy support + e
200
What are conditions required for paired sample t-tests?
1. Continuous data
2. Same individuals or matched pairs of individuals
3. Normal distribution
4. ~ equal variance between groups
200
When would your drop a variable from the correlation matrix when doing multiple regression?
If there is too high correlation with another variable, you could run into multicollinearity. Multicollinearity violates the assumption for this regression model and can lead to increased standard errors, unreliable coefficient estimates, and misleading significance values.
300
Money' = 200 + 3.75 years
For this expression, if making a scatterplot of money versus years, what would the computer display the line of best fit slope as?
3.75
300
Write out the unstandardized regression equation for perceived amount learned
Perceived amount learned = 0.58 rapport + 0.12 autonomy support + e
300
Come up with an experimental design in which we use a paired samples t-test
We generally can use paired sample t tests to compare the mean scores of two groups both assessed using a continuous variable (matching criteria), or the same group tested at two time points or under different conditions.
A good example a paired sample t-test would be useful in is comparing anxiety levels in patients given a medication compared to those given a placebo.
300
Generally, how do you interpret a variable's regression coefficient when reading a regression table? Write out a sentence.
For all other variables held constant, a 1-unit increase in that specific predictor, is, on average, associated with a (insert coefficient here) increase/decrease in (insert outcome variable).
400
The graph below has a (linear/non-linear) form. To find the correlation between the two variables (Pearson's r / Spearman's rho) is the more appropriate test.
linear, Pearson's r
400
Write the unstandardized regression equation for expected final grade?
Perception = 0.09 rapport + 0.20 autonomy support + e
400
What are the two wilcoxon tests used as non-parametric t-tests, and what are the corresponding parametric t-tests?
Wilcoxon rank sum --> Independent samples t-test
Wilcoxon signed rank test --> Paired samples t-test
400
What are a few of the residual diagnostics that are necessary to perform when doing multiple regression analysis?
Scatter plot of residuals vs predicted values, histogram of residuals, normality plot of residuals, QQ plot, etc.
500
Explain what the effect size of a regression model and regression slope is (beyond the answer, what the answer actually means)
Effect size = the size (magnitude) of the relationship between the independent variable and the dependent variable
For regression model, use R squared or adjusted R squared as effect size
Regression slope = change in outcome variable with one-unit change in the predictor variable (use standardized beta for effect size)
500
Write the unstandardized regression equation for actual final grade
Actual final grade = 0.02 rapport + 0.17 autonomy support + e
500
There is a research group that is looking into the differences between Harvard students and Yale students in biology knowledge. In a survey, Harvard students had a mean score of 82.3% and Yale students had a mean of 45.5%. The 95 percent confidence interval is [-6.3, 2.4]. Do we reject or fail to reject the null hypothesis?
Since the confidence interval contains that value 0, we automatically fail to reject the null hypothesis.
500
If the graph for the predicted/fitted values against the residual of a regression model is distributed randomly, what can you conclude?
Probably no auto-correlation (homogenous variances)