Sabinas lecture 1 to 7

Question 1

Variance & SD

Answer 1

Variance & SD
sigma2 or V = the degree to which a variable ‘varies’ around its
mean V = sum (X-X)2/N-1 = SS/df
SD = squ root sigma 2 or  V (in the same units, easier to interpret)

Question 2

› Covariance

Answer 2

CoV = the degree to which two variables ‘vary’ simultaneously or co-vary
Note: the variance of a variable is… its covariance with itself.

Question 3

Correlation

Answer 3

degree of linear
relationship between two variables and, essentially, it is a
standardised covariance

Question 4

Continuous versus discrete variables

Answer 4

continuous and discrete (categorical)

Question 5

Regression sum of sqares

Answer 5

Regression sum of sqares is about something we can predict. (1-R2) is what we can not predict.

Question 6

how to work out t

Answer 6

b/ SEb = t

Question 7

df Residual

Answer 7

df residual is proportion of the variable we cannot predict. N-K-1 predictors.

Question 8

Confidence Intervals (CI)

Answer 8

b is an estimate of the population parameter. Ultimately, we want to know the true value of the regression coefficient. Having the CI helps to illustrate this idea (i.e., if we conducted this research 100 times, there is XX% chance that the true (yet unknown) slope is within the specified range of values) .

Question 9

how to use CIs

Answer 9

If the range includes 0, then we can conclude that the findings are NOT n statistically significant, and vice versa.
› We can also use the CI to test whether the slope is different from a particular value (e.g., whether this slope is different from the one found in previous studies).
› SPSS does not calculate CI automatically

CI is sort of our parameter line. If I perform the experiment 100 times, this is the range I expect the B to be in.

Question 10

Converting from b to β [in italics!]

Answer 10

ß = b x (SDx/SDy)
b = ß x √(Vx/Vy)

Question 11

If B is equal to zero

Answer 11

there is no equation. It is not important. It will still be featured in the regression equation (DO NOT TAKE IT OUT).
The most common null hyp is that b = zero. Slope is not different to zero, nothing systematic is happening.

It doesn’t have to be zero, the slope is stagnant. Is the new slope different to 1.5 or not? If the CI includes this, it is fine as a null hyp.

Question 12

MR advantages

Answer 12

Can use both categorical and continuous independent
variables
› Can easily incorporate multiple independent variables
› Is appropriate for the analysis of experimental or
nonexperimental research

Question 13

Factors Affecting the Results

of the Regression Equation

Answer 13

Sample size (N)
The amount of scatter of points around
the regression line [indexed by (Y-Y’)2
or SSresidual] = Other things being equal, the smaller
SSresidual, the larger SSregression, and
hence larger the F-ratio

›The range of values in the X variable,
indicated by (X-X)2

Question 14

Assumptions Underlying MR (only a

glimpse now)

Answer 14

Dependent variable is a linear function of the IVs
- can be overlooked if one selects extreme cases of X… selection of only extreme cases can ‘force’ the regression to appear linear, even if it might be curvilinear for the X values. Bad practice…
› Each observation is drawn independently
› Errors are normally distributed
› The mean of errors is = 0
› Errors are not correlated with each other, nor with the IV
› Homoscedasticity of variance
- Variance of errors is not a function of IVs
- The variance of errors at all values of X is constant, meaning that it is the same at all levels of IV

Question 15

reg df

Answer 15

number of IVS

Question 16

do you report the non significant parts in regression conclusion?

Answer 16

YES

Question 17

decimal places for b

Answer 17

three decimal places. .003 etc

Question 18

what happens when you shorten the effect sample line graph?

Answer 18

B is same, ß changes. distribution is different so SDs change

Question 19

why is ß the same as ry2 when the two IVs don’t correlate

Answer 19

because the overlap is not in the ven diagram. ß = ry2 when r12= 0

Question 20

assumptions of error

Answer 20

we assume that they are normally distributed, independent,

and have constant variance.

Question 21

regression line

Answer 21

that the IVs are differentially weighted
so that the prediction is optimised and the sum of the errors2 of prediction is minimised.
That is, the sum of squared values for each residual term is smaller than for any other
possible straight line, thus the term least squares

Question 22

ß way of writing conc

Answer 22

standard scores or stand deviations. not standard units

Question 23

what is a different metric

Answer 23

includes different scale of same dimension like cm is DIFF to hours. cm is DIFF to meters. must be exactly the same or use beta

Question 24

when is something not a common cause

Answer 24

a, b and c paths equivalent to ß’s, where DV is VarY, and it is regressed on Variables X1 and X2
› If VarX1 has no effect on Y (b=0), but it has an effect on X2, then:
- it is not a common cause
- ßYX2 = r YX2 = c
- c does not change with the inclusion or exclusion of X1
- OR
- If VarX1 has no effect on X2 (a=0),
but it has an effect on Y, then:
- it is not a common cause
- ßYX2 = r YX2 = c
- c does not change with the inclusion or exclusion of X1

Question 25

importance of r2

Answer 25

For explanation, a high R2 less important than proper
variable selection

R2 should be within expected range
- Explaining 25% of the variance may be surprisingly high for some questions, low for others
› A high (?) R2 is important for prediction
› “Human freedom may then rest in the error term

Question 26

Indirect Effects

Answer 26

The regression weight for Parent Education changed
because a mediating variable (Previous Achievement) was included in the model.
› A portion of the direct effect from the first regression is now indirect (e.g., paths d and a)
› Mediating variables do not have to be included to interpret regression coefficients as effects
› However, this type of regression only focuses on
direct effect.

Question 27

mean when you standardise something

Answer 27

every time you standardise something the mean will be very close to zero like z score distribution

Question 28

what do you look at when you have intercorrelations output?

Answer 28

Correlations that our IVs have with our DV

- Correlations that our IVs have with each other

Question 29

including a common cause

Answer 29

prevents inflating the other variables bs and ßs

Question 30

df for change statistics in sequential

Answer 30

always 1 because only adding 1 vriable at a time

Question 31

order of entry

Answer 31

the variable entered first has the most opportunity to capture the higherst proportion of variance. the one entered last has a tiny ∆R2

Question 32

total effects

Answer 32

the direct effect plus e x d (the indirect effects lines timsed together)

Question 33

importnce measure btter than ∆R2

Answer 33

√∆R2

Question 34

Unique Variance

Answer 34

Some researchers add each variable last in a sequential regression to determine its “unique” effect/variance
› Can get the same information in simultaneous regression, requesting semipartial (part) correlations
› Square the part correlations to determine unique variance

Question 35

what to do with stepwise

Answer 35

large N and cross validation necessary

Question 36

interactions and curevs

Answer 36

Test for interactions by sequentially adding a cross-product
term to the regression
› Test for curves in the regression plane by sequentially adding
powers of variables (e.g., variable2)

Question 37

purpose sequential

Answer 37

Is a variable (or block of variables) important for an outcome?
- Does a variable explain/predict variance beyond that
explained by other influences?
- Does a variable explain/predict unique variance in an
outcome?
- Test for statistical significance of interactions and curves
- Does a variable aid in predicting some criterion

Question 38

What to Interpret in sequential

Answer 38

magnitude = importance √∆R2,

stat significancec ∆R2

Question 39

when to use sequential

Answer 39

Useful for explanation when guided by theory
› Useful for testing interactions & curves
› Estimates total effects in implied model
› More ‘similar’ to ANOVA method (?)

be careful with order

Question 40

alternatives to Stepwise

Answer 40

Simultaneous regression
› Sequential regression (final equation)
› Study correlations between IVs. If some are highly
intercorrelated, consider combining them in a composite.
› SEM (…?…)