Lecture 4_MLR, sr^2, pr, Flashcards Preview

*Biostatistics II > Lecture 4_MLR, sr^2, pr, > Flashcards

Flashcards in Lecture 4_MLR, sr^2, pr, Deck (33)
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1
Q

What are the building blocks of

multiple linear regression (MLR)?

A

Correlation coefficients (r)

2
Q

The Regression Line (2 predictors)

A

Y’ = a + b1X1 + b2X2
• Y′ is the predicted value of the DV, Y.
• a is the intercept of the regression line.
• b1 and b2 are the partial regression coefficients for the predictor variables X1 and X2, respectively

3
Q

What is Y’ in the regression equation for 2 predictors?

A

the predicted value of the DV, Y.

4
Q

What are b1 and b2 in the regression equation for 2 predictors?

A

the Partial regression coefficients for the predictor variables X1 and X2, respectively

5
Q

In a path diagram, what does the e path represent?

A

(1 - R²) the coefficient of non-determination

• error not explained by the model

6
Q

In a path diagram, what does the curved, double-headed arrow between two predictors represent?

A

the bivariate correlation between the 2 variables.
• indicates that the researcher is not going to explain the correlation between X1 & X2, but acknowledges that it is not zero.

7
Q

In a path diagram, what do squares represent?

A

measured variables

8
Q

In a path diagram, what do circles represent?

A

Factors (latent variables hypothesized by “fun” math)

9
Q

In a path diagram, what do the straight single-headed arrows represent?

A

the standardized coefficient (β) between the particular predictor variable (IV) and the outcome variable (DV)

10
Q

A path model must have …

A

a coefficient for every arrow

11
Q

What is the interpretation for the partial regression coefficient?

A

the expected change in the outcome variable (DV) when the predictor variable (IV) changes by 1 unit, controlling for all other predictor variables (holding all other IVs constant)

12
Q

Why can we not compare the partial regression coefficients (b) to determine the relative importance of each predictor variable (IV)?

A

the size of b is influenced by the scale/metric in which the IV is measured, and may be different for each IV

13
Q

What do the standardized regression coefficients (β) indicate?

A

the relative influence of the IVs in the equation.
• the expected change in the DV (in st. dev. units) when the IV changes by one st. dev. unit, holding all other IVs constant

14
Q

Which is better for comparing across groups, b or β? Why?

A

comparisons across groups should be based on bs and not βs.

• βs are population specific; they are sensitive to fluctuations in variances and covariances across populations

15
Q

What does the Squared multiple correlation (R²) represent?

A

the proportion of variance in the DV accounted for by all the IVs

16
Q

What does the Standard Error of the Estimate express?

A

the amount, on average, that the predicted value of Y will deviate from the observed value (Obtained from R² and the standard deviation of the DV)

17
Q

When will R² be equal to the sum of the squared bivariate correlations?

A

When the 2 predictors are not correlated with one another (r12 = 0)

18
Q

What does the squared semipartial (part) correlation relate?

A
  • how much R² will increase when a predictor is added last to the model
  • the unique contribution of a predictor to the variance explained by the model
19
Q

When predictors are correlated with each other, what will give us the unique proportion of variance in Y that is attributable to each predictor in the model?

A

Squaring the semipartial correlations

20
Q

How can we calculate an estimate of the explained variance that is ambiguous?

A

Take the difference between R² and the sum of all semipartial correlations

21
Q

Given the correlation matrix, means, and standard deviations of the variables, what can we calculate?

A

the regression coefficients (standardized and unstandardized), R² and the St. Error of the Estimate

22
Q

What is the notation for a zero-oreder (Pearson) correlation?

A

r12, rY1, rY2, etc

23
Q

What is the notation for a partial correlation?

A
prY1 = rY1.23
prY2 = rY2.1
pr12 = r12.Y34
24
Q

What is the notation for a Semipartial correlation?

A
srY1 = rY(1.23)
srY2 = rY(2.1)
sr12 = r1(2.Y34)
25
Q

What does the order (zero-order, first-order, second order, etc.) of a correlation coefficient (r, sr, pr) indicate?

A

the number of variables that have been “partialed” out
• rY1 = zero-order
• rY2.1 = first-order [also rY(2.1)]
• rY1.23 = second-order

26
Q

What is a partial correlation (pr)?

A

the correlation between two variables with the influence of one (or more) other variables removed from Both.

27
Q

What does the squared partial correlation between the DV and an IV express?

A

unique variance of the IV as a proportion of previously unexplained variance in the DV

28
Q

For a given set of variables in a MR, which will be larger (in absolute value): the partial correlation or the semipartial correlation?

A

the partial correlation (think about the difference in the denominators)
sr = a/(a + b + c + d)
pr = a/d

29
Q

What are 2 interpretations for e?

A
  • the error in prediction.

* Or a transformed version of Y with the influence of the predictor(s) removed, or partialed out.

30
Q

What is an alternative method for a partial correlation using SPSS?

A

Run 2 regressions:

  1. regress one variable, IV(1), onto other IVs whose effects want removed and save residuals as a new variable (new residual variable is a transformation of the original variable with the influences of the other two removed
  2. repeat for 2nd variable, DV (dido)
  3. correlate new IV(1) and DV residual variables
31
Q

What does the correlation between the two residual variables tell us?

A

the partial correlation between IV(1) & DV when the influences of other IV have been removed from both of them.

32
Q

What are 2 measures of how well regression model fits our data?

A

* size of the SE of the estimate

33
Q

What are the units of the SE of the estimate?

A

the units in which the DV is measured