EDF 5400

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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

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

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?

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?

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

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 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

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

Multiple regression….

Y’ = bX + a

Y’ = b1X1 + b2X2 + a

Y’ = b1X1 + b2X2 + b3X3 + a

Multiple regression with SPSS...

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?

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)