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Research methods Term 2 > Multiple Regressions - L1 > Flashcards

Multiple Regressions - L1 Flashcards

1
Q

What is a correlation?

A

An association or dependency between two independently observed variables

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2
Q

What diagram would we use for a correlation?

A

Scatter plot ( each data point is a single subject)

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3
Q

What is the score associated with the analysis of correlation called?

A

Pearson correlation coefficient.

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4
Q

What would the PCC be when x and y are completely independent of eachother?

A

0.0

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5
Q

What would the PCC be when x and y are identical?

A

1.0

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6
Q

What would the PCC be when x and y are completely inverse?

A

-1.0

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7
Q

What PCC score are we looking for?

A

1.0, the more similar the values of variables x and y are, the greater the covariance!

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8
Q

What is Partial Correlation?

A

Partial correlation is a measure of the strength and direction of a linear relationship between two continuous variables whilst controlling for the effect of one or more other continuous variables

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9
Q

What diagram would we use for a Partial correlation?

A

When information from different variables is overlapping, we can visualise this problem as a Venn diagram

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10
Q

What does each circle represent in a partial correlation venn diagram?

A

Size of circle represents the variance of variable
Overlap of circles represents a correlation between variables

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11
Q

What is the main difference between multiple linear regression and correlation?

A

it describes the relationship between one or more predictor variables (X,X2, etc) and a single criterion variable (Y)

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12
Q

What is the regression equation?

A

Y= ax +b, where a is the slope and b is the y- intercept.

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13
Q

What is prediction error E?

A

the difference between the actual values Y and the predicted value Y (with a squiggle on top)

E = Y - Y(squiggle)

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14
Q

What is our objective with a regression model?

A

Our objective is to find the best fit between the model and the observations, by adjusting the values of B, until the prediction error is minimised.

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15
Q

How would you assess the Goodness of fit of a regression model? (all three)

A

Multiple correlation coefficient ®

Coefficient of Determination (R2)

F-ratio

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16
Q

How would you assess the Goodness of fit of a regression model? (R)

A

Correlation between the predicted values Y(squi) and the observed values (Y)

17
Q

How would you assess the Goodness of fit of a regression model? (R2)

A

The proportion of variance of explained by the regression model
This is simply the square of the multiple correlation coefficient

18
Q

How would you assess the Goodness of fit of a regression model? (F)

A

As for ANOVA, we can derive an F-ratio contrasting the proportion of explained variance with the residual variance, allowing a statistical test

Similar to an ANOVA, the F-ratio reflects the ratio of explained variance against total variance. If this is unlikely to be explained by chance alone (e.g. p<0.05), we speak of a significant effect

19
Q

What do higher F-Ratios show?

A

Higher F-ratios indicate better models:
improved prediction of Y (triangle on top) over Y (dash on top) indicated by MSm

Decreased prediction error, indicated by MSr

20
Q

How is effect size for a multiple regession estimated?

A

By using Cohens F2

21
Q

What is Cohens F2 value for a SMALL effect size?

A

0.02

22
Q

What is Cohens F2 value for a MEDIUM effect size?

A

0.15

23
Q

What is Cohens F2 value for a LARGE effect size?

A

0.35

24
Q

What are the Multiple Regression Approaches?

A

Simultaneous (standard)
Stepwise
Hierarchical

25
Q

What are the 6 Factors that effect Multiple linear regression?

A

Outliers
Scedasticity
Singularity & Multicollinearity
Number of observations / Number of predictors
Range of values
Distribution of values

26
Q

What measures the extremetiy of an outlier?

A

Cook’s distance measures the extremity of an outlier, values over 1 are a cause for concern

27
Q

What is Homoscedasticity?

A

residuals stay relatively constant over the range of the predictor variable

28
Q

What is Heteroscedasticity?

A

residuals vary systematically across the range of the predictor variable

29
Q

How can Heteroscedacity be evaluated?

A

Heteroscedacity can be evaluated using a plot of the predicted value Y (triangle) vs the residual error (Y resid)

30
Q

What is Multicollineraity?

A

refers to a high similarity between two or more variables (r>0,9)

31
Q

What is singularity?

A

refers to a redundant variable, typically, this results when one variable is a combination of two or more other variables (eg subscores of an intelligence scale)

32
Q

What are some issues with multic and singularity?

A

Logical: dont want to measure the same thing twice

Statistical: cannot solve regression problem because the system is ill-conditioned

33
Q

What is Anscombe’s Quartet?

A

This is Range and distribution

Research methods Term 2 (2 decks)

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