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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

Albert OosterhofSeptember 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...


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 determinedSupplement 9


Plot z-scores and regression equationSupplement 9


Estimating Y using z-scoresSupplement 9


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


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 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 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 beif the correlation had been.......

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


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 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 ......

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...

+3

+3

…if r = +1.00

+2

+2

+1

+1

0

0

-1

-1

-2

-2

-3

-3


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 mean...

+3

+3

…if r = +1.00

+2

+2

+1

+1

0

0

-1

-1

-2

-2

-3

-3


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 mean...

+3

+3

…if r = +0.75

+2

+2

+1

+1

0

0

-1

-1

-2

-2

-3

-3


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 mean...

+3

+3

…if r = +0.50

+2

+2

+1

+1

0

0

-1

-1

-2

-2

-3

-3


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 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 2


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 2


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 2


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


Predicting Y when given X.....


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, sy = 4.47 and sx = 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 = ?


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…...

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


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 1st ExampleSupplement 9


2nd ExampleSupplement 9


Error in prediction (residual)


Error in Prediction, i.e. ResidualSupplement 9


Error in Prediction, i.e. ResidualSupplement 9


Error in Prediction, i.e. ResidualSupplement 9


Standard Error of EstimateSupplement 9


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


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


Standard error of estimate for raw-scores


Standard Error of Estimate

Standard deviation of Y scores for a given X score


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 EstimateSupplement 10


3-dimensional scatter plots…. Supplement 10


3-dimensional scatter plots…. Supplement 10


3-dimensional scatter plots…. Supplement 10


3-dimensional scatter plots…. Supplement 10


Multiple regression….

Y’ = bX + a

Y’ = b1X1 + b2X2 + a

Y’ = b1X1 + b2X2 + b3X3 + a

Multiple regression with SPSS...


Back to bivariate correlation and regression...


Correlations between...

  • …pretest and posttest?

  • …pretest and estimated posttest?

  • …pretest and residual?


Explained and Unexplained Components of Variance

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


Explained and Unexplained VarianceSupplement 10


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 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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