Statistical Methods for Psychology

518 Chapter 15 Multiple Regression Table 15.1 (continued) State Expend PTratio Salary PctSAT SAT PctACT ACT Nebraska 5.935 14.5 ...

Figure 15.1 Histograms, Q-Q plots, and scatter plots of the variables used in this example 15.1 Multiple Linear Regression 519 3 ...

520 Chapter 15 Multiple Regression Two Variable Relationships The most obvious thing to do with these data is to ask about the r ...

In addition, the percentage of students taking the SAT varies drastically from state to state, with 81% of the students in Conne ...

Coefficientsa Unstandardized Standardized Coefficients Coefficients Model B Std. Error Beta t Sig. 1 (Constant) 1089.294 44.390 ...

discuss is labeled “Model Summary.” From the summary you can see that when Expend is the sole predictor the correlation between ...

which they will never be. We need the intercept because it forces the average of our predic- tions to equal the average of the o ...

We know that if we ran the simple regression predicting SAT from LogPctSAT alone, the resulting set of predicted scores would re ...

or, in terms of the variables we have been using I obtained the predicted scores from and stored the predicted scores as PredSAT ...

coefficient (slope) that we obtain is the same coefficient we find in the multiple regres- sion solution. We can think of the m ...

width of the confidence interval and decreases the tvalue for that coefficient. This is what is measured by the VIF. Moreover, w ...

difference between those states on any other variable. If we now solved for our regression coefficients using the standardized v ...

Then to test For a test on the regression coefficient of Expend, we have This is a standard Student’s t on N 2 p 21 5 50 – 2 21 ...

and is denoted as or or. In Exhibit 15.1 it is given as the error term in the analysis of variance summary table as 664.646. The ...

15.6 The Multiple Correlation Coefficient Exhibit 15.1 shows that the multiple correlation between SAT and two predictors (Expen ...

Testing the Significance of R^2 We have seen how to ask whether each of the variables is making a significant contribution to th ...

correlation of .30 would require 187 subjects for the same degree of power. As you can see, a reasonable amount of power require ...

some would not reach it, but the points could be fit reasonably well by this plane. The ver- tical distances of the points from ...

predictor variable. In other words, whereas the partial correlation ( ) has variable 2 partialled out of both the criterion and ...

significant contribution. That does not mean that it would not contribute to any other model predicting SAT. (In fact, when used ...