W5: RQ for Predictions 2

Question 1

What is a full regression equation involving 2 IVs

Answer 1

Yi = a + b1X1i + b2X2i + ei

Question 2

What is a model regression equation involving 2 IVs

Answer 2

Y^i = a + b1X1i + b2X2i

Question 3

What is an intercept in a regression equation. What is it signified by

Answer 3

a. Expected score on DV when all IVs = 0

Question 4

What is a partial regression coefficient in a regression equation. What is it signified by

Answer 4

b1, b2. Expected change in IV variable for each unit change in an IV, holding constant scores on all other IV

Question 5

What is the Sum of Squares in a regression equation. What is SS Total Indicated by

Answer 5

SStotal = SSreg + SSres

Question 6

What is the aim of OLS. Use sum of squares to explain

Answer 6

Maximize SSreg; Minimize SSres

Question 7

What is R^2.

Answer 7

Effect size measuring strength of prediction.

Question 8

Formula of R^2. And what does it mean? What is another name for R^2

Answer 8

R^2 = SSreg/SStotal.

R&2 is the proportion of SStotal account for by SSreg.

Another name: Coefficient of Determination

Question 9

What is the range of R^2

Answer 9

0 to 1. Closer to 1 = Stronger

Question 10

To calculate a confidence on R^2, what are the 4 things we require

Answer 10

1. ) Estimated R^2 value
2. ) Numerator df (no. of IVs)
3. ) Denominator df (n-IVs-1)
4. ) Desired confidence level

Question 11

Typically what is the biasness/consistency of R^2

Answer 11

IT is often biased, but consistent

Question 12

How is an adjusted R^2 better than R^2

Answer 12

It is usually less biased, but we should always report both values

Question 13

How do we make meaningful comparison between IVs in a multiple regression

Answer 13

1. ) Transform regression coefficient to STANDARDIZED PARTIAL regression coefficient (z-scores)
2. ) Semi-Partial Correlations as effect size esimate

Question 14

Making meaningful comparison between IVs in a multiple regression: Transform regression coefficient to STANDARDIZED PARTIAL regression coefficient (z-scores)… When interpreting coefficients, what is the difference. When is this method useful?

Answer 14

Coefficients are interpreted in SD units

Example: One SD increase in variable X will increase in 0.5 SD decrease in variable Y.

Only useful when IV has an arbitrary scaling

Question 15

Making meaningful comparison between IVs in a multiple regression: Transform regression coefficient to STANDARDIZED PARTIAL regression coefficient (z-scores)… What is the intercept

Answer 15

Always 0

Question 16

Making meaningful comparison between IVs in a multiple regression: Semi-Partial Correlations. Overview.

Answer 16

Correlation between DV and EACH focal IV, when effects of other IVs have been removed from focal IV.

Question 17

Making meaningful comparison between IVs in a multiple regression: Semi-Partial Correlations. What is the SQUARED semipartial correlation

Answer 17

Indicates proportion of variation in DV uniquely explained by each IV.

Question 18

What are the 4 statistical assumptions underlying the linear regression model

Answer 18

1. ) Independence of Observations
2. ) Linearity
3. ) Constant variance of residuals/ homoscedastiscity
4. ) Normality of Residual Scores

ILHN I love Honey Nougats

Question 19

Statistical Assumption Linear Regression: Independence of Observations. How do we meet this

Answer 19

Met usually as long as

1. ) Scores are not duplicated for bigger sample
2. ) Responses on one variable does not determine person’s response to another variable

Question 20

Statistical Assumption Linear Regression: Linearity. How do we meet this. There are 4 ways

Answer 20

1. ) Scatterplot Matrix
2. ) Scatterplot of Residual Scores
3. ) Marginal Model Plots
4. ) Marginal Conditional Plots

Question 21

Statistical Assumption Linear Regression: Linearity. Scatterplot Matrix

Answer 21

Defined by variables being assigned to rows (Y-Axis) or Column (X-axis)
Examine scatter plots where DV is on the Y-Axis.

Non-Linearity would be a U shape.

Question 22

Statistical Assumption Linear Regression: Linearity. Scatterplot of Residual Scores

Answer 22

Scatterplot of Residual Scores against

(1) Observed IV scores
(2) Predicted scores on DV

Question 23

Statistical Assumption Linear Regression: Linearity. Marignal Model Plot

Answer 23

Marginal model plots of scores on the DV (Y) against scores on each IV and on predict scores (on X)

Question 24

Statistical Assumption Linear Regression: Linearity. Marignal Conditional Plot. Why is it especiallyg good

Answer 24

It shows partial regression line after other IVs are partialled out.

Question 25

Statistical Assumption Linear Regression: Homoscedasticity, What are the 2 ways

Answer 25

1,) Residual Plots (Similar to linearity)

2.) Breusch-Pagan Test

Question 26

Statistical Assumption Linear Regression: Homoscedasticity, Residual Plots

Answer 26

Even distribution of residuals

Question 27

Statistical Assumption Linear Regression: Homoscedasticity, Breusch-Pagan Test Overview

Answer 27

Null-Hypothesis Test that assumes the variance of residuals are constant/homoscedastic

Question 28

Statistical Assumption Linear Regression: Homoscedasticity, Breusch-Pagan Test. What happens when the P value is small

Answer 28

We have reason to reject the assumption of constant variance for the residuals

Question 29

Statistical Assumption Linear Regression: Normality of Residuals. What are the 3 ways

Answer 29

1. ) qqplot
2. ) Histogram
3. ) boxplot

Question 30

Statistical Assumption Linear Regression: Normality of Residuals. qqplot. What does it contain

Answer 30

Middle line: Strict normality
Side Lines: confidence

See residuals inside confidence

Question 31

Statistical Assumption Linear Regression: Normality of Residuals. qqplot. What must we look out for

Answer 31

1. ) Outliers: Vary large studentized residual value in absolute terms (High standard deviation)
2. ) influential Case: If removed from analysis, results in regression coefficient changing notably in value

Question 32

Statistical Assumption Linear Regression: Normality of Residuals. qqplot. How do we find influential cases

Answer 32

Cook’s D as a measure of overly influential values.

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