Correlations
What is the range of possible values for a simple correlation?
-1 to 1
What will the intercept be equivalent to in an intercept-only model (i.e., a model with no predictors)?
Mean of y
How would a model R2 of .26 be interpreted?
26% of the variance in y can be accounted for by the predictors in the model.
A squared standard deviation is the...
variance
What should you bring to take the exam?
How would you interpret a simple correlation of r = .9 between variables x and y?
x and y have a strong, positive, linear relationship
OR
As x increases, y increases as well.
What is another name for the model R2?
Squared multiple correlation/SMC
How would a p-value of .002 associated with a test of a partial coefficient be interpreted? (t = 3.5)
Over repeated sampling, assuming that null hypothesis that there is no association between x1 and y, adjusting for x2, is true, we would expect to obtain a result as or more extreme than the one obtained (t=3.5) 0.2% of the time.
The correlation between x and y-hat is ______.
1
What is the difference between Type 1 and Type 3 sums of squares?
In Type 1 SS, Variables are entered sequentially into the model. In Type 3 SS, variables are entered simultaneously into the model.
How are a partial and semipartial correlation different from one another?
In a partial correlation, both y and x are residualized so that they do not contain the variance accounted for by a third variable (denominator is partial variance of y).
In a semipartial correlation, only x is residualized (denominator is full variance of y).
What approach is used when entering predictors in an MLR model (e.g., sequential, hierarchical, simultaneous)?
Simultaneous/Type III SS
How would you interpret a 95% confidence interval of [3, 20] for a partial coefficient?
Over repeated sampling, 95% of similarly constructed CIs as [3, 20] would contain the true partial coefficient representing x1's association with y when excluding its shared variance with x2.
t2 = ?
F-statistic when numerator df=1
Why can it be troublesome to compute confidence intervals for R2 in traditional ways?
R2 is bounded between 0 and 1, meaning that it won't be normally distributed, particularly when the population rho-squared is actually 0 or close to 0.
What is the interpretation of a squared semipartial correlation of sr2 = .32 between x1 and y, adjusting for x2?
When adjusting for the shared variance between x1 and x2, the remaining variance of x1 accounts for 32% of the total variance in y.
Which equations are incorrect? Why?
See OneNote for equations.
Equations 2 and 4 are incorrect.
What is the difference between a decision, a conclusion, and an interpretation within the context of hypothesis testing, p-values, and confidence intervals?
Decision: reject/fail to reject the null
Conclusion: Within the context of the study, what does the decision lead us to believe?
Interpretation: What does the actual p-value or confidence interval mean?
True or False: The semipartial correlation will always be equivalent to or greater than the partial correlation (when representing the same variables/relationships).
The standard error of the estimate is also known as ______.
the root mean squared error.
What are two different methods for finding a semipartial correlation/squared semipartial correlation?
1. Residualizing
2. Increment in R2
What type of correlation are coefficients within an MLR model akin to?
Semipartial correlation
Which of the following elements is not needed in an interpretation of a p-value?
A. The p-value itself (or some transformation of it)
B. "Over repeated sampling"
C. Assuming that the null is true (and stating the null)
D. The alpha level/type 1 error rate for your hypothesis test
D
The squared correlation between y and y-hat is _____.
the model R2 or squared multiple correlation (SMC)
What is the standard error of the estimate? In other words, how would you (informally) interpret the standard error of the estimate?
It's the standard deviation of the residuals for the model, meaning that on average, each actual data point differs from the predicted data point by this much.