Multiple Linear Regression (MLR) Flashcards
How can we detect variable that co-vary
scatter plots, causion of cause or effects, always think of potential third variable
statistical analysis of co-variants CANT distinguish between, spurious, causal and common process reasons
statistical analysis of co-variants CANT distinguish between, spurious, causal and common process reasons
Covariance doesn’t tell us about _________. So always use _________________
independence; scatter plots
Covariance is _______________ sensitive, so we use the _________________ values in place of the raw data, this makes all scales have mean_________ and standard deviation ____, and is called _________________________________
size; standardised, 0, 1, Pearson’s product moment correlation coefficient
what is effect size
a quantitative measure to allow comparisons between studies, this is given by r squared
aka coefficient of determination
r squared is the proportion of variance that one variable explains in another
how to find the slope of regression
find the slope that gives the minimum error variance: the least squares approach to regression
what is partial correlation
the amount of variance in X3 that is related to X1 and X1 alone
‘How much of the X3 variance that is not explained by other variables is explained by X1’
‘partial out’ the variability explained by X2
look at how much remaining variability in X3 is explained by knowing the remaining variability in X1
take out the variability using simple linear regression
a pure measure uncontaminated by other variables
uniqueness of variance makes theoretically simpler
reveal hidden relationships
what is semipartial correlation
how much of the total variance of X3 does X1 and X1 alone explain
a more intuitive baseline
allows easy comparison of coefficients because X3 is constant
Give an example of an misleading schematics on illustrating partial correlation
- No correlation (r=0) between desirability (X1) and frequency of buying (X3)
- Positive correlation (r=0.5, r^2=0.25) btw amount of pocket money (x2) and buying frequency (X3)
- Negative correlation (r=-0.4, r^2=0.16) btw desirability (X1) and pocket money (X2)
- from Venn diagram, partial correlation r3.2 should be zero
- but calc
r13. 2 = (r13-r12r32)/ rt((1-r12^2)(1-r32^2)) = 0.252
partial correlation uncovering hidden relationships when ____________________________
two components / factors influence a third in opposite ways
How to regard ANOVA as regression
In ANOVA, looking to see if ‘knowing’ the level of the factor (IV) explains variability of the DV
In regression, looking to see if ‘knowing’ the score of the IV explains var of DV
ANOVA talks about a level mean, e.g., 3 different levels of coffee consumption (1cup, 2cup…), to do regression, you take a measure of how much coffee they had and now you have a continuous variable
Why can ANCOVA be seen as a kind of partial correlation
In ANOVA: have DV and factor, factor explain some var of DV, the unexplained var is the SSerror
Idea of covariate is to ‘remove’ unwanted var in DV, some DV var is attributed to CV and hence removed from the SSerror
Covariate is the X2 here
Multiple linear regression describes the relationship between \_\_\_\_\_ variables Have \_\_\_\_\_\_\_\_\_\_ predictors (X1,X2...) and \_\_\_\_\_\_\_\_\_\_ DV (Y) Effect size (R^2), is the proportion of variance of Y (the DV) explained knowing \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
multiple variables
2 or more predictors, 1 DV
all of the predictors
Multiple linear regression
with 1 predictor, describe data as _______
with 2 predictors, describe data as ___________
use ___________ method with k predictors
1 predictor, describe data as a line
2 predictors, describe data as a surface
use least squares method with k predictors
Curvilinear regression
with single predictor, __________________
with single predictor, restricted range of curves
