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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

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
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

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!
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

slide42

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

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

multiple regression
Multiple regression….

Y’ = bX + a

Y’ = b1X1 + b2X2 + a

Y’ = b1X1 + b2X2 + b3X3 + a

Multiple regression with SPSS...

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?

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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