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Prediction/Regression

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1 Prediction/Regression
Chapter 12 Prediction/Regression Part 3: Nov. 21, 2013

2 Multiple Regression Bivariate prediction – 1 predictor, 1 criterion
Multiple regression – use multiple predictors Reg model/equations are same, just use separate reg coefficients () for each predictor Ex) multiple regression formula with three predictor variables a is still the regression constant (where the reg line crosses the y axis) b1 is the regression coefficient for X1 b2 is the regression coefficient for X2, etc…

3 Standardized regression coefficients
With bivariate regression, we discussed finding the slope of the reg line, b. b = unstandardized regression coefficient based on the original scale of measurement But we’re sometimes interested in comparing our regression results to other researchers’ …may have same variables but used different measures Standardized regression coefficients (β or beta) will let us compare (more generalizable)

4 Using standardized coefficients (betas)
There is a formula for changing b into β in the chapter, but you won’t be asked to use it So the regression equation (model) would look like this if we use standardized regression coefficients (β):

5 Overlap among predictors
Common for there to be correlation among predictor variables β = unique contribution of each variable β1 = unique contribution of X1 in predicting Y, excluding overlap w/other predictors R2 gives the % variance in y explained by all of the predictors together There will be a significance test for R2 to determine whether the entire regression model explains significant variance in Y. If yes  Then examine the individual predictors’ β There is a signif test for each of these. Is each predictor important or only some of them?

6 Interpreting beta In general, interpret it like a correlation between predictor & criterion: if β is positive, higher scores on predictor (x) are related to higher scores on criterion (y) If β is negative, higher scores on x go with lower scores on y.

7 Hypothesis tests for regression
We are usually interested in multiple issues Is the β significantly different from 0? (is there any relationship betw x & y?) In multiple regression, we may be interested in which predictor is the best (has the strongest relationship to the criterion)

8 Prediction in Research Articles
Multiple regression results commonly reported Note example table in book, reports r’s and βs for each predictor; reports R2 in note at bottom.

9 Reporting mult. regression
From previous table… The multiple regression equation was significant, R2 = .13, p < Depression (β = .30, p<.001) and age (β = .20, p < .001) both significantly predicted intragroup effect, but number of sessions and duration of the disorder were not significant predictors. This indicates that older adults and those with higher levels of depression had higher (better) intragroup effects.

10 SPSS Reg Example Analyze Regression  Linear
Remember, “Independent Variable” is your predictor (x), “Dependent Variable” is your criterion (y) Class handout of output – what to look for: “Model Summary” section - shows R2 ANOVA section – 1st line gives ‘sig value’, if < .05  signif This tests the significance of the R2 (is the whole regression equation significant or not? If yes  it does predict y) Coefficients section – 1st line gives ‘constant’ = a Other lines give ‘standardized coefficients’ = b or beta for each predictor For each predictor, there is also a significance test (if ‘sig’ if < .05, that predictor is significantly different from 0 and does predict y) If it is significant, you’d want to interpret the beta (like a correlation)


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