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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... regression line....

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 scores from pretest scoresz-scores to show how the slope (b) and intercept (a) are determinedSupplement 9

Plot scores from pretest scoresz-scores and regression equationSupplement 9

Estimating scores from pretest scoresY using z-scoresSupplement 9

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

What would we predict scores from pretest scoresY 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 scores from pretest scoresY 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 scores from pretest scoresY 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: scores from pretest scoresWhat would we predict Y to beif the correlation had been.......

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

Redundant: scores from pretest scoresWhat would we predict Y to beif the correlation had been.......

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

What if

Redundant: scores from pretest scoresWhat 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 scores from pretest scoresY 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... scores from pretest scores

+3

+3

…if r = +1.00

+2

+2

+1

+1

0

0

-1

-1

-2

-2

-3

-3

Regression towards the mean... scores from pretest scores

+3

+3

…if r = +1.00

+2

+2

+1

+1

0

0

-1

-1

-2

-2

-3

-3

Regression towards the mean... scores from pretest scores

+3

+3

…if r = +1.00

+2

+2

+1

+1

0

0

-1

-1

-2

-2

-3

-3

Regression towards the mean... scores from pretest scores

+3

+3

…if r = +0.75

+2

+2

+1

+1

0

0

-1

-1

-2

-2

-3

-3

Regression towards the mean... scores from pretest scores

+3

+3

…if r = +0.75

+2

+2

+1

+1

0

0

-1

-1

-2

-2

-3

-3

Regression towards the mean... scores from pretest scores

+3

+3

…if r = +0.75

+2

+2

+1

+1

0

0

-1

-1

-2

-2

-3

-3

Regression towards the mean... scores from pretest scores

+3

+3

…if r = +0.50

+2

+2

+1

+1

0

0

-1

-1

-2

-2

-3

-3

Regression towards the mean... scores from pretest scores

+3

+3

…if r = +0.50

+2

+2

+1

+1

0

0

-1

-1

-2

-2

-3

-3

Regression towards the mean... scores from pretest scores

+3

+3

…if r = +0.50

+2

+2

+1

+1

0

0

-1

-1

-2

-2

-3

-3

Predicting Y when given X..... scores from pretest scoresSupplement 8, page 2

Predicting Y when given X..... scores from pretest scoresSupplement 8, page 2

Predicting Y when given X..... scores from pretest scoresSupplement 8, page 2

Predicting Y when given X..... scores from pretest scoresSupplement 8, page 2

Predicting Y when given X..... scores from pretest scoresSupplement 8, page 2

Predicting Y when given X..... scores from pretest scoresSupplement 8, page 2

Predicting Y when given X..... scores from pretest scoresSupplement 8, page 2

Predicting Y when given X..... scores from pretest scoresSupplement 8, page 2

Predicting Y when given X..... scores from pretest scoresSupplement 8, page 2

Predicting Y when given X..... scores from pretest scoresSupplement 8, page 2

Predicting Y when given X..... scores from pretest scores

4 scores from pretest scores

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 scores from pretest scoresr = .75, sy = 4.47 and sx = 2.24, slope is adjusted from .75 to b = ?

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

If scores from pretest scoresb = 1.5, a = ?Take advantage of what we know about regression…...

If scores from pretest scoresb = 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 scores from pretest scoresb = 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 scores from pretest scoresst ExampleSupplement 9

2 scores from pretest scoresnd ExampleSupplement 9

Error in prediction (residual) scores from pretest scores

Error in Prediction, i.e. Residual scores from pretest scoresSupplement 9

Error in Prediction, i.e. Residual scores from pretest scoresSupplement 9

Error in Prediction, i.e. Residual scores from pretest scoresSupplement 9

Standard Error of Estimate scores from pretest scoresSupplement 9

Standard error of estimate… scores from pretest scoresz-scores versus raw-scores

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

Standard error of estimate scores from pretest scoresfor raw-scores

Standard Error of Estimate scores from pretest scores

Standard deviation of Y scores for a given X score

Standard Error of Estimate scores from pretest scoresSupplement 10

Standard deviation of Y scores for a given X score

Using SPSS to find regression equation and standard error

Standard Error of Estimate scores from pretest scoresSupplement 10

3-dimensional scatter plots…. scores from pretest scoresSupplement 10

3-dimensional scatter plots…. scores from pretest scoresSupplement 10

3-dimensional scatter plots…. scores from pretest scoresSupplement 10

3-dimensional scatter plots…. scores from pretest scoresSupplement 10

Multiple regression…. scores from pretest scores

Y’ = bX + a

Y’ = b1X1 + b2X2 + a

Y’ = b1X1 + b2X2 + b3X3 + a

Multiple regression with SPSS...

Back to bivariate correlation and regression... scores from pretest scores

Correlations between... scores from pretest scores

- …pretest and posttest?
- …pretest and estimated posttest?
- …pretest and residual?

Explained and Unexplained Components of Variance scores from pretest scores

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

Explained and Unexplained Variance scores from pretest scoresSupplement 10

Proportion scores from pretest scores 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 scores from pretest scores 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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