Statistical Analysis for Education and Psychology Researchers

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8.10

where Ŷ, the predicted value obtained from the regression equation when xi=8 is the same
as in the previous example (124.285), Spred is the estimated standard deviation of
individual values of y when x is the specified value xi, and,

The 95 per cent CI is therefore 124.285−[2.306×5.5024] to 124.285+[2.306×
5.5024]=111.596 to 136.974.

Interpretation

We would be 95 per cent confident that a pupil with a teacher estimated maths ability
score of 8 would have a standardized maths attainment score within the interval 112 to

137. Notice that the interval width for prediction of an individual score is larger than the
     width when predicting a mean score. These prediction intervals can be plotted for each
     case in the data set, and if they are compared with a similar plot for the mean response, it
     will be seen that the confidence intervals for the individual predictions are much wider
     (see Figure 8.7c). The confidence interval does not include zero which indicates that a
     teacher’s estimate of a pupil’s maths ability is a significant predictor of that pupil’s
     attainment on a standardized maths test.

Computer Analysis

Whereas the worked examples demonstrate the general principles of regression analysis,
it is clear that such computations are both time consuming and tedious to perform. In
most research situations the researcher will use a propriety statistical package to perform
these analyses. The same data and the same regression model is now analysed using the
least squares regression procedure in SAS called PROC REG. In this section the
appropriate SAS code is described and related to the tests for regression assumptions. In
the next section interpretation of the output is discussed.
The procedure PROC REG is a general purpose interactive procedure in SAS that fits
linear regression models by least squares. PROC REG can also produce scatter plots of
variables, diagnostic plots and regression and diagnostic statistics. The parameter
estimates in the linear model are adjusted to optimize the model fit.
Assuming that the data has been input screened and edited and an initial regression
model formulated which is based on theoretical/empirical considerations, an extension of
IDA means standard deviations and corrected sums of squares should be calculated for all

Statistical analysis for education and psychology researchers 268