Adv Correlat Methods 7Th Quiz (Week 9- Feb 25-29) Exam 2 Cont'd

Front 1

Describe the components of the linearity assumption.

Back 1

1. There is a linear relationship between Y and the predictors.

2. The slope of the relationship between x and predicted y is the same (constant), regardless of the value of the other variables.

Front 2

How do you test for linearity?

Back 2

Examine a residual plot.
The residual plot involves placing the standardized residuals on the Y axis and the standardized predicted values on the X axis.

(This is the graph with the horizontal zero error line and lots of points clustered above and below it).

Ze = standardized residuals
Zyhat= standardized predicted values.

Front 3

How do you know if there is a violation of the linearity assumption?

Back 3

You'll see a curve in the residual plot. Most residuals will be above the zero line at some predicted values and below zero at others.

Front 4

Discuss homoskedasticity and heteroskedasticity in terms of their relative desirability for MLR.

Back 4

homoskedasticity is good, heteroskedasticity is bad.

Front 5

Discuss potential violations of the linearity assumption.

Back 5

1. interaction. When X1 changes, y changes one amount at one level and a different amount at another level(?) This means that predicting y depends upon the level of another variable.
2. curvilinear relationship.

Front 6

Describe the components of the linearity assumption.

Back 6

1. There is a linear relationship between Y and the predictors.

2. The slope of the relationship between x and predicted y is the same (constant), regardless of the value of the other variables.

Front 7

How do you test for linearity?

Back 7

Examine a residual plot.
The residual plot involves placing the standardized residuals on the Y axis and the standardized predicted values on the X axis.

(This is the graph with the horizontal zero error line and lots of points clustered above and below it).

Ze = standardized residuals
Zyhat= standardized predicted values.

Front 8

How do you know if there is a violation of the linearity assumption?

Back 8

You'll see a curve in the residual plot. Most residuals will be above the zero line at some predicted values and below zero at others.

Front 9

Discuss homoskedasticity and heteroskedasticity in terms of their relative desirability for MLR.

Back 9

homoskedasticity is good, heteroskedasticity is bad.

Front 10

Discuss potential violations of the linearity assumption.

Back 10

1. interaction. When X1 changes, y changes one amount at one level and a different amount at another level(?) This means that predicting y depends upon the level of another variable.
2. curvilinear relationship.

Front 11

Discuss what we would hope to see on a residual plot and what it means.

Back 11

y = Ze (Standardized residuals)
x = Zy (standardized predicted values)

We want errors to fall equally above and below the line. That means that we are better at predicting y.

Front 12

What would heteroskedasticity look like on a residual plot?

Back 12

megaphone shape

Front 13

What are 2 problematic things that you might see on a residual plot?

Back 13

1. curvilinear relationship
2. Megaphone shape to the errors (this means heteroskedasticity)

Front 14

If you see a curvilinear relationship on a residual plot (strd residuals vs. strd predicted values) what do you need to do?

Back 14

If there is a curvilinear relationship to the errors, including x^2 or x^3 term might allow you to caputre the relationship in order to better predict y. (this process is polynomial regression?)

Front 15

What do you do if you detect nonlinearity?

Back 15

1. try polynomial regression
2. try a nonlinear transformation of y
3. If there is a nonlinear regression relationship, but the distribution of error terms is normal and the error terms are homoskedastic, then transform x instead of y.

Front 16

Describe the homoskedasticity assumption.

Back 16

1. There are equal variances for residuals across each value of the IVs.

2. There is constant scatter around e=0.

Front 17

If you see a megaphone shape in your error points on the residual plot, what does this tell you?

Back 17

you have heteroskedasticity

there is a greater error of measurement at some levels of the IV than at others.

Front 18

On a residual plot of vacation spending versus family income, the error points are megaphone shaped. How do you correct for this?

Back 18

Use an interaction term (here, the interaction term will be level of enjoyment of vacation: low, mid, high. Errors cluster more closely around each of these three seperate lines).

Front 19

For a megaphone-shaped residual plot, what does adding an interaction term do?

Back 19

Adding an interaction term helps to reduce the heteroskedasticity of error variance.

Front 20

What are the three central testing assumptions in MLR?

Back 20

1. linearity assumption
2. homoscedasticity assumption
3. assumption of normality of errors

Front 21

How do you test for homoscedasticity?

Back 21

Plot standardized residuals (Ze) on y axis and standardized predicted values (Zy hat) on x axis.

Front 22

Residual plots allow you to test for:

Back 22

1. linearity
2. homoskedasticity

Front 23

How do you identify a violation of homoscedasticity?

Back 23

you see megaphone shape in residual plot.

Front 24

What might cause a violation of homoscedasticity?

Back 24

1. nonnormality of a variable
2. one variable related to some transformation of another
3. greater error of measurement at some levels of an IV than at others. (this is the situation for which you have to add intxn term).

Front 25

What is the assumption of normality of errors?

Back 25

Errors will be normally distributed across each value of the IVs.

Front 26

How do you test for normality of errors?

Back 26

Use SPSS output to look at histogram of residuals, PP plot, QQ plot.

Front 27

If you use SPSS output to look at histogram of residuals, PP plot, QQ plot, which MLR assumption are you testing?

Back 27

Assumption of normality of errors

Front 28

If you plot standardized residuals (Ze) on the y axis and standardized predicted values (Zy) in order to get a residual plot, what assumptions of MLR are you testing?

Back 28

linearity assumption
homoskedasticity assumption

Front 29

This plot rank orders residuals and compares them to the rank order of residuals expected from a normal distribution.

Back 29

PP Plot

Front 30

This plot compares standardized residuals to expected values.

Back 30

QQ plot

Front 31

Describe what good/bad histograms and PP plots look like.

Back 31

Good histogram = normally distributed
Bad histogram = skewed (highest point off center, to left or right)

Good PP plot: points form straight diagonal line
Bad PP plot: points form a curvy line.

Front 32

the potential to change the slope

Back 32

leverage

Front 33

have unusual values on the independent variable

Back 33

outliers

Front 34

A point that is high in leverage....

Back 34

is unusual in its value on the independent variable

Front 35

Looks at the distance/diference between predicted y and observed y.

Back 35

discrepancy

Front 36

On a graph for which a diagonal line has been drawn through a cloud of points, the point that falls directly above the mean (and far above the cloud of points) can be characterized in what ways based upon discrepancy and leverage?

Back 36

This point is high in discrepancy and low in leverage.

Front 37

For a cloud of points through which a diagonal line has been drawn, a point that is far to the right of the cloud of point but is still along the line of the diagonal (if the diagonal line were extended beyond the cloud of points) can be said to have what qualities in terms of discrepancy and leverage?

Back 37

High in leverage (change slope), but low in discrepancy (difference in predicted y and obs y).

Front 38

For a cloud of data points through which a diagonal line has been drawn, a point that is not above the mean and not immediately beyond the diagonal would be considered to be what (in terms of discrepancy and leverage)

Back 38

High in leverage (change slope), and high in discrepancy (difference in predicted y and obs y). This means that this is an influential data point.

Front 39

This type of point is high in both leverage and discrepancy.

Back 39

influential data pt

Front 40

This type of point is particularly likely to change regression coeficients and impact the slope.

Back 40

influential data pt

Front 41

If we keep a point that is high in discrepancy but low in leverage in the regression equation, what will happen.

Back 41

If this type of point is above the mean, the regression constant will go up.
If this high discrepancy, low leverage point is below the mean, the regession constant will go down.

Front 42

How do you know if there is a violation of normality of errors with the histogram of residuals?

Back 42

Residuals should be normally distributed in the histogram.

Front 43

How do you know if there is a violation of normality of errors with the PP and QQ plots?

Back 43

In PP and QQ plots, the points for the cases should fall along the diagonal running from lower left to upper right. If the pts are way off line (often below the line at one end and above at the other end) there's a violation.

Front 44

What do you do if you detect nonnormality?

Back 44

First, correct nonconstant error variance first to see if it fixes the problem.

Most transformations that correct for heteroscedasticity also correct for non-normality.

Front 45

Most transformations that correct for _____ also correct for _____.

Back 45

Most transformations that correct for heteroscedasticity also correct for non-normality.

Front 46

A point that is high in leverage is...

Back 46

far from the mean on the IV.

Front 47

A point that is highly discrepant has...

Back 47

a big difference between observed y and predicted y.

Front 48

This is the number of SDs by which predicted y (y hat) would change if we deleted case i.

Back 48

DIFITS(Difference in fit, standardized).

Front 49

Indicates how much deleting this case effects each individual b (for instance, b for variable X1, b for variable X2, etc).

Back 49

DF Beta

Front 50

this is at the mean of all of your variables

Back 50

centroid

Front 51

We are looking at cases that are far from the cetroid when determining...

Back 51

Mahalonobis distance

Front 52

What are outliers?

Back 52

1. Cases that do not fit the pattern of data
2. points that are far from the mean of x or y or both
3. in SLR, an observation whose DV value is unusual given the value of the IV.

Front 53

What are the consequences of having outliers in my data?

Back 53

1. Outliers may not be predicted well by the regression line, so they have large residual values.
2. Outliers may influence the regression line (by impacting either the regression constant or the slope)
3. Outliers may lead to type I and II errors
4. Outliers may lead to results that do not generalize except to another sample with the same type of outlier.

Front 54

How do I detect possible outliers in my data?

Back 54

Examine cases with large standardized scores on one or more variables (z>3.29 or simply disconected from the other z scores). This helps you examine a person who is way out of range

2. Examine the split for your dichotomous variables to make sure it's not terribly uneven

3. use graphical methods- histograms, box plots, normal probability plots. Outliers will appear to be far away from the rest of the data points

4. Examine studentized residuals

5. Examine studentized deleted residual (t1)

Front 55

In a residual plot, points that fall ______ are potential outliers.

Back 55

In a residual plot, points that fall far away from the regression surface (e=0) are potential outliers.

Front 56

Most of these fall between -3 and 3 on the standardized normal curve

Back 56

studentized residuals

Front 57

How do you create studentized residuals (which are used to detect outliers)?

Back 57

To create studentized residuals, you must standardize the residuals by dividing by the standard error of the residuals.

Front 58

When creating a studentized deleted residual...

Back 58

1. delete case i from the regression and compute the regression
2. use that regression solution to compute error for case i, this is the deleted residual
3. studentize by dividing by its standard error.

Front 59

Why can it be difficult to detect outliers?

Back 59

Sometimes, outliers can be well predicted by the line.

Also, when you run a regression, an outlier might shift the line by influencing the slope, so it might not look like an outlier.

Front 60

This statistic is distributed as a t distribution with (n-k-2) df, so we can formally test for outlier status.

Back 60

studentized deleted residual

Front 61

What is the question that we are asking when we look for an influential data point?

Back 61

When I take this case out, does it change the slope of the line, b?

Front 62

What are influential data points?

Back 62

1. cases that exert an influence on the position of the regression line
2. The removal of an IDP will result in a significant change in the regression.
3. Are both highly discrepant and have high leverage

Front 63

Influence on coefiecients =

Back 63

discrepency * leverage

Front 64

How do I test for influence?

Back 64

see how much regression coeficients change when a case is deleted.

Front 65

Measures the observation's influence on the regression coefficients

Back 65

Cook's distance

Front 66

Represents the difference between the bs (slope) when the case is and is not included in the regression.

Back 66

Cook's distance

Front 67

How do I know if I have an influential Data point?

Back 67

1. Cases with influence scores larger than 1 are suspected of being outliers.

2. Formal test: Cook's distance is distributed similar to an F stat with (k+1,n-k-1)df. (h0= cases do not change the regression coeficients).

Front 68

What do I do if I have Influential Data points?

Back 68

1. Exclude them (but this could lead to unstable regression coeficients).
2. Examine curvilinear relationships or interactions
3. try a transformation

Front 69

How do I test for high leverage data points?

Back 69

1. Use hat values
2. Use a related index called Mahalonobis distance
3. Use the mean shift outlier model (not discussed much in class).

Front 70

Index of how much a single case can impact predicted Ys

Back 70

hat values (which are used to test for high leverage data points).

Front 71

If the hat value is large for a particular case, then...

Back 71

that case has a big impact on the fitted values.
(hat values are used when testing for high leverage data points).

Front 72

Hat values range from...

Back 72

1/n to 1

Front 73

In SLR, hat values measure distance from __, while in MLR, hat values measure distance from__.

Back 73

In SLR, hat values measure distance from the mean of X, while in MLR, hat values measure distance from the centroid.

Front 74

What is the centroid?

Back 74

Centroid = point at the intersection of the means of all the variables in multivariate space.
In MLR, hat values measure distance from the centroid.

Front 75

Measures the distance of a case from the centroid of the remaining cases

Back 75

Mahalonobis distance

Front 76

Mahalonobis distance tests for what type of data points?

Back 76

high leverage data pts

Front 77

Mahalonobis distance allows you to evaluate for each case using a _________

Back 77

Chi square distribution.

Front 78

As hat values reach one, what does this mean?

Back 78

Hat values approaching one have the potential to exert a big influence on the line.

Front 79

The further away from the centroid they get, hat values ____.

Back 79

increase.

Hat values increase the further from the centroid that they get.