An APA-Style Results Section for Multiple Regression

Results for a Single Set of Predictors

A multiple regression analysis was conducted to evaluate how well the strength measures predicted physical injury level. The predictors were the five strength indices, while the criterion variable was the overall injury index. The linear combination of strength measures was significantly related to the injury index, F(5, 94) = 4.18, p < .01. The sample multiple correlation coefficient was .43, indicating that approximately 18% of the variance of the injury index in the sample can be accounted for by the linear combination of strength measures.

In Table 1, indices to indicate the relative strength of the individual predictors are presented. All the bivariate correlations between the strength measures and the injury index were negative, as expected, although only four of the five indices were statistically significant (p < .05). Only the partial correlation between the strength measure for the gluteus/hamstring muscles and the injury index was significant. On the basis of these correlational analyses, it is tempting to conclude that the only useful predictor is the strength measure for the gluteus/hamstring muscles. It alone accounts for 15% (-.392 = .15) of the variance of the injury index, while the other variables contribute only an additional 3% (18% - 15% = 3%).

 
           


Results for Two Unordered Sets of Predictors

Two multiple regression analyses were conducted to predict the overall injury index. One analysis included the three lower-body strength measures as predictors (quadriceps, gluteus/hamstrings, and the abdominal/lower back), while the second analysis included the two upper-body strength measures (arms/shoulders and grip strength). The regression equation with the lower-body measures was significant, R2 = .16, adjusted R2 = .13, F (3, 96) = 6.07, p < .001. However, the regression equation with the upper-body measures was not significant, R2 = .06, adjusted R2 = .04, F(2, 97) = 3.06, p = .051. Based on these results, the lower-body measures appear to be better predictors of the injury index.

Next, a multiple regression analysis was conducted with all five strength measures as predictors. The linear combination of the five strength measures was significantly related to the injury index, R2 = .18, adjusted R2 = .14, F(5, 94) = 4.18, p < .005. The lower-body strength measures predicted significantly over and above the upper-body measures, R2change = .12, F(3, 94) = 4.69, p < .001, but the upper-body strength measures did not predict significantly over and above the lower-body measures, R2 change = .02, F(2, 94) = 1.29, NS. Based on these results, the upper-body measures appear to offer little additional predictive power beyond that contributed by a knowledge of lower-body measures.

Of the lower-body strength measures, the strength measure for the gluteus/hamstring muscles was most strongly related to the injury index. Supporting this conclusion is the strength of the bivariate correlation between the gluteus/hamstring measure and the injury index, which was - .39, p < .001, as well as the comparable correlation partialling out the effects of the other two lower-body measures, which was -.33, p < .005.


Results for Two Ordered Sets of Predictors

A multiple regression analysis was conducted to predict the overall injury index from previous medical difficulties and age. The results of this analysis indicated that medical difficulties and age accounted for a significant amount of the injury variability, R2 = .16, F(2, 97) = 9.35, p <.001, indicating that older women who had more medical problems tended to have higher scores on the overall injury index.

A second analysis was conducted to evaluate whether the strength measures predicted injury over and above previous medical difficulties and age. The five strength measures accounted for a significant proportion of the injury variance after controlling for the effects of medical history and age, R2 change = .15, F(5, 92) = 3.97, p < .005. These results suggest that women who have similar medical histories and are the same age are less likely to have injuries if they are stronger.


Tips for Writing an APA Results Section for Multiple Regression

Here are some guidelines for writing a results section for multiple regression analyses. Some researchers initially provide a description of the general overall analytic strategy that includes different regression analyses conducted to answer the research questions. This general description is necessary to the degree that the analyses are unconventional, complex or both.
The steps required to write a results section:

  (1) Describe the test or tests, the variables, and the purpose of the test or tests.
  • For example: “A multiple regression analysis was conducted to predict the overall injury index from previous medical difficulties and age.”
  • Describe the independent or predictor variables. If the variables can be divided into conceptually distinct sets, describe the predictors in each set.
  • In addition, indicate whether the sets are ordered or nonordered.
  • Describe what the criterion variable is.
  (2) Report the descriptive statistics (e.g., means, standard deviations, and bivariate correlations). These statistics may be reported prior to the presentation of the multiple regression analyses or in conjunction with them (e.g., along with the standardized beta weights).
  • If you are reporting only a few correlations, report them in the text (e.g., r (98)= .39, p < .001).
  • For regression analyses, there are often many bivariate correlations. These statistics can be summarized in tabular form. Typically, you would present the lower diagonal of a correlation matrix. Means and standard deviations for the variables also can be reported in the table.
  (3) Report the results of the overall regression analyses. If several analyses have been conducted, report the results for each one separately.
  • Report the effect size (e.g., R2 = .43) for each overall test and the significance test associated with it. Also consider reporting the adjusted R2. If sets of predictors are evaluated, report the changes in R2 and the significance tests associated with those changes in R2.
  • Report the standard error of estimate if the dependent variable has a meaningful metric.
  (4) Describe and summarize the general conclusions of the overall analysis.
For example: “The multiple regression results suggest that women who have similar medical histories and are the same age are less likely to have injuries if they are stronger.”
  (5) Report the contributions of the individual predictors.
  • Consider relevant statistics to evaluate the relative importance of each predictor.
  • Typically, the standardized regression coefficients, the partial correlations, or both are presented in a table.
  • Report whether the individual variables make a significant contribution to the prediction equation (e.g., t(98) = -3.l3, p < .001).
  (6) Present the results graphically, if possible. You may present graphs to show relationships among variables. The graph should be inserted in the text where appropriate. For example, if the graph pertains to assumptions, you would insert it in the section where you discuss assumptions.

 


Last update: April 19, 2004