Statistical Analysis for Education and Psychology Researchers

3 An initial regression model based on background information or theoretical considerations is then fitted to the data and a reg ...

theoretical or empirical considerations and common sense. For example, an educational researcher may want to know whether indivi ...

Test Assumptions for Regression Analysis Inferences based on hypothesis tests for the regression slope, intercept, and overall m ...

regression line) and overlaying this with a plot of observed values of the response variable against the independent variable. T ...

education, a dummy variable, coded as less than bachelor’s degree versus bachelor’s degree or more. Results of this regression a ...

reported that initial exploratory analyses, ‘eliminated several other potentially influential independent variables...on the bas ...

Regression analysis would be inappropriate when there are only ten cases and is performed here for illustrative purposes only. M ...

119 14161 5 25 595 95 9025 1 1 95 118 13924 6 36 708 ΣY^2 =134202 ΣX^2 =374ΣXY=6686 ΣY=1154 ΣX=56 n=10 The corrected sums of squ ...

—8.6 The variation of the response variable, Y, about the fitted regression line is called the sums of squared residuals and is ...

Significance Tests and Confidence Intervals Significance test for overall model fit For a simple linear regression model with on ...

The statistic RMSE is an estimate of the variation of the response variable about the population regression line. It is sometime ...

Interpretation With a significance level of 5 per cent, a two-tailed test, and df=8 (10–2), the critical t- value shown in Table ...

Confidence Interval Limits for the Predicted Mean Response The 95 per cent CI limits for the predicted mean response with a fixe ...

— 8.10 where Ŷ, the predicted value obtained from the regression equation when xi=8 is the same as in the previous example (124. ...

variables in the candidate model. The following SAS code produces these statistics for the two variables SMATHS and MATHS. proc ...

The first line of code, PROC REG, is the beginning of the regression procedure. The next line contains the model statement which ...

Figure 8.1: Overlay plot of response vs. explanatory and predicted vs. explanatory variables The normality assumption is checked ...

Figure 8.2: Normal probability plot of residuals The assumption of constant variance of errors is checked by plotting residuals ...

proc plot; plot r*id=‘*’/vref=0; title 'Plot of Residuals vs Case Number (id)'; run; The SAS output is shown in Figure 8.4. Figu ...

Figure 8.5: Plot of residual vs. maths score (explanatory variable) The regression output produced by PROC REG for the maths dat ...