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EDF 5400. Albert Oosterhof September 27 and October 2. Create the scatterplot for these scores, then plot the regression line.... Supplement 8. Adding the regression line to the scatterplot. A scatterplot and regression line typically involves more than five cases.

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Edf 5400

EDF 5400

Albert OosterhofSeptember 27 and October 2


Create the scatterplot for these scores then plot the regression line supplement 8

Create the scatterplot for these scores, then plot the regression line....Supplement 8


Adding the regression line to the scatterplot

Adding the regression line to the scatterplot...


A scatterplot and regression line typically involves more than five cases

A scatterplot and regression line typically involves more than five cases...


Here is the regression equation for predicting posttest scores from pretest scores supplement 9

Here is the regression equation for predicting posttest scores from pretest scoresSupplement 9


We will switch to z scores to show how the slope b and intercept a are determined supplement 9

We will switch to z-scores to show how the slope (b) and intercept (a) are determinedSupplement 9


Plot z scores and regression equation supplement 9

Plot z-scores and regression equationSupplement 9


Estimating y using z scores supplement 9

Estimating Y using z-scoresSupplement 9


Interpret predicted y scores with respect to standard deviations from the mean

Interpret predicted Y scores with respect to standard deviations from the mean?


What would we predict y to be if the correlation had been

What would we predict Y to beif the correlation had been.......

r = .50 and X was 1.0 SD above the mean?

r = .50 and X was 2.0 SDs above the mean?

r = .50 and X was 3.0 SDs above the mean?

r = .50 and X was 1.0 SD below the mean?

r = .50 and X was 3.0 SDs below the mean?

r = .50 and X was 0.5 SDs above the mean?

r = .50 and X was 0.0 SDs above the mean?


What would we predict y to be if the correlation had been1

What would we predict Y to beif the correlation had been.......

r = .10 and X was 1.0 SD above the mean?

r = .10 and X was 3.0 SDs above the mean?

r = .10 and X was 1.0 SD below the mean?

r = .10 and X was 0.0 SDs above the mean?


What would we predict y to be if the correlation had been2

What would we predict Y to beif the correlation had been.......

r = 1.00 and X was 1.0 SD above the mean?

r = 1.00 and X was 3.0 SDs above the mean?

r = 1.00 and X was 1.0 SD below the mean?

r = 1.00 and X was 0.0 SDs above the mean?


Redundant what would we predict y to be if the correlation had been

Redundant: What would we predict Y to beif the correlation had been.......

  • r = .50 and X was 1.0 SD above the mean?


Redundant what would we predict y to be if the correlation had been1

Redundant: What would we predict Y to beif the correlation had been.......

r = .50 and X was 1.0 SD above the mean?

What if


Redundant what would we predict y to be if the correlation had been2

Redundant: What would we predict Y to beif the correlation had been.......

r = .50 and X was 1.0 SD above the mean?

What if

r = .50 and X was 3.0 SDs above the mean?

What if


What would we predict y to be if

What would we predict Y to be if ......

r = .10 and X was 1.0 SD above the mean?

r = 1.00 and X was 1.0 SD above the mean?

r = 1.00 and X was 3.0 SDs above the mean?

r = 0.50 and X was 1.0 SD below the mean?

r = 0.50 and X was 2.0 SDs above the mean?

r = 0.50 and X was at the mean?


Regression towards the mean

Regression towards the mean...

+3

+3

…if r = +1.00

+2

+2

+1

+1

0

0

-1

-1

-2

-2

-3

-3


Regression towards the mean1

Regression towards the mean...

+3

+3

…if r = +1.00

+2

+2

+1

+1

0

0

-1

-1

-2

-2

-3

-3


Regression towards the mean2

Regression towards the mean...

+3

+3

…if r = +1.00

+2

+2

+1

+1

0

0

-1

-1

-2

-2

-3

-3


Regression towards the mean3

Regression towards the mean...

+3

+3

…if r = +0.75

+2

+2

+1

+1

0

0

-1

-1

-2

-2

-3

-3


Regression towards the mean4

Regression towards the mean...

+3

+3

…if r = +0.75

+2

+2

+1

+1

0

0

-1

-1

-2

-2

-3

-3


Regression towards the mean5

Regression towards the mean...

+3

+3

…if r = +0.75

+2

+2

+1

+1

0

0

-1

-1

-2

-2

-3

-3


Regression towards the mean6

Regression towards the mean...

+3

+3

…if r = +0.50

+2

+2

+1

+1

0

0

-1

-1

-2

-2

-3

-3


Regression towards the mean7

Regression towards the mean...

+3

+3

…if r = +0.50

+2

+2

+1

+1

0

0

-1

-1

-2

-2

-3

-3


Regression towards the mean8

Regression towards the mean...

+3

+3

…if r = +0.50

+2

+2

+1

+1

0

0

-1

-1

-2

-2

-3

-3


Predicting y when given x supplement 8 page 2

Predicting Y when given X.....Supplement 8, page 2


Predicting y when given x supplement 8 page 21

Predicting Y when given X.....Supplement 8, page 2


Predicting y when given x supplement 8 page 22

Predicting Y when given X.....Supplement 8, page 2


Predicting y when given x supplement 8 page 23

Predicting Y when given X.....Supplement 8, page 2


Predicting y when given x supplement 8 page 24

Predicting Y when given X.....Supplement 8, page 2


Predicting y when given x supplement 8 page 25

Predicting Y when given X.....Supplement 8, page 2


Predicting y when given x supplement 8 page 26

Predicting Y when given X.....Supplement 8, page 2


Predicting y when given x supplement 8 page 27

Predicting Y when given X.....Supplement 8, page 2


Predicting y when given x supplement 8 page 28

Predicting Y when given X.....Supplement 8, page 2


Predicting y when given x supplement 8 page 29

Predicting Y when given X.....Supplement 8, page 2


Predicting y when given x

Predicting Y when given X.....


What we have been doing

4

3

2

1

Z-score: WEIGHT

0

-1

-2

-3

-3

-2

-1

0

1

2

3

Z-score: HEIGHT

What we have been doing!


For r 75 s y 4 47 and s x 2 24 slope is adjusted from 75 to b

For r = .75, sy = 4.47 and sx = 2.24, slope is adjusted from .75 to b = ?


For r 75 s y 4 47 and s x 2 24 slope is adjusted from 75 to b1

For r = .75, sy = 4.47 and sx = 2.24, slope is adjusted from .75 to b = ?


If b 1 5 a take advantage of what we know about regression

If b = 1.5, a = ?Take advantage of what we know about regression…...


If b 1 5 a take advantage of what we know about regression1

If b = 1.5, a = ?Take advantage of what we know about regression…...

r = .75 and zx = .00, predicted zy = ?

r = .75 and zx = .00, predicted zy = .00

r = 1.00 and zx = .00, predicted zy = ?

r = 1.00 and zx = .00, predicted zy = .00

r = .00 and zx = .00, predicted zy = ?

r = .00 and zx = .00, predicted zy = .00


Edf 5400

If b = 1.5, a = ?Taking advantage of what we know about regression, and remembering that if zX = 0, predicted zY = .00Supplement 9, 2nd page – Example 1


Summary of 1 st example supplement 9

Summary of 1st ExampleSupplement 9


2 nd example supplement 9

2nd ExampleSupplement 9


Error in prediction residual

Error in prediction (residual)


Error in prediction i e residual supplement 9

Error in Prediction, i.e. ResidualSupplement 9


Error in prediction i e residual supplement 91

Error in Prediction, i.e. ResidualSupplement 9


Error in prediction i e residual supplement 92

Error in Prediction, i.e. ResidualSupplement 9


Standard error of estimate supplement 9

Standard Error of EstimateSupplement 9


Standard error of estimate z scores versus raw scores

Standard error of estimate… z-scores versus raw-scores


Z scores and raw scores the general case

z-scores and raw scores...the general case


Standard error of estimate for raw scores

Standard error of estimate for raw-scores


Standard error of estimate

Standard Error of Estimate

Standard deviation of Y scores for a given X score


Standard error of estimate supplement 10

Standard Error of EstimateSupplement 10

Standard deviation of Y scores for a given X score

Using SPSS to find regression equation and standard error


Standard error of estimate supplement 101

Standard Error of EstimateSupplement 10


3 dimensional scatter plots supplement 10

3-dimensional scatter plots…. Supplement 10


3 dimensional scatter plots supplement 101

3-dimensional scatter plots…. Supplement 10


3 dimensional scatter plots supplement 102

3-dimensional scatter plots…. Supplement 10


3 dimensional scatter plots supplement 103

3-dimensional scatter plots…. Supplement 10


Multiple regression

Multiple regression….

Y’ = bX + a

Y’ = b1X1 + b2X2 + a

Y’ = b1X1 + b2X2 + b3X3 + a

Multiple regression with SPSS...


Back to bivariate correlation and regression

Back to bivariate correlation and regression...


Correlations between

Correlations between...

  • …pretest and posttest?

  • …pretest and estimated posttest?

  • …pretest and residual?


Explained and unexplained components of variance

Explained and Unexplained Components of Variance

What variability in weight is explained versus not explained by variability in height?


Explained and unexplained variance supplement 10

Explained and Unexplained VarianceSupplement 10


Proportion of variance explained and unexplained r 2 and 1 r 2

Proportion of Variance Explained and Unexplainedr2and1-r2

Questions…

  • On graph, what variance on Y is explained by variance on X ? What variance is unexplained?

  • On the graph, where is standard error of estimate illustrated?

  • On the graph, how can be describe the criterion of least squares?

  • On the graph, what would we see if the correlation increased or decreased?


Proportion of variance explained and unexplained r 2 and 1 r 21

Proportion of Variance Explained and Unexplainedr2and1-r2

Not only height and weight…

  • Study time and test scores (r =.7)

  • GRE scores and grades (r =.4)

  • Boat registrations and manatee kills (r =.9)

  • Heights of husbands and wives (r =.6)


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