Advanced Statistics
Simple Linear Regression Example
This page shows an example of a simple linear regression using the hsb2.sav
dataset. The model regresses write on read. The regression equation looks like this,
write = 23.959 + 0.552*read
The constant 23.959 is the expected value of write when read equals zero. And the
regression coefficient, 0.552, tells us that the every one unit increase in
read the expected value of write increases by 0.552 points.
Here is the regression equation with the standardized coefficient,
z-score(write) = 0.597*z-score(read)
The standardized regression coefficient tells us that for every one standard
deviation increase in read there will be an expected increase in write of
0.597 standard deviations in write.
Below is the SPSS syntax file and output for the complete simple linear
regression example.
get file='/Users/ender2/data/spss/hsb2.sav'.
regress
/descriptives=mean stddev n
/statistics=r coeff anova outs ci f
/dependent=write
/method=enter read
/residuals=outliers(zresid) normprob(zresid) histogram(zresid)
/scatterplot=(*zresid, *zpred)
/save pred zpred zresid cook sdbeta .
Notes:
- The /residual option requests several standardized residual reports
including a table of outliers, normal probability plot and histogram.
- The /scatterplot option requests a residual versus fitted (predicted) plot.
- The /save option requests predicted scores, standardized predicted scores,
standardized residuals,
Cook's D (a measure of influence), and standardized dfbeta (anoter measure of influence).
SPSS output