# 73 Regressions

## Linear Regression

As you will see in journal articles, regression results are often reported in tables. This is due to the fact that a typical regression usually comprises many independent variables and more than one model. A typical regression table usually lists the independent variables in the rows and beta coefficients (b) with standard Errors (s.e) in parentheses in the columns. Significant coefficients are indicated with asterisks. Beta coefficients and standard errors are also organized in columns according to the model (where there are multiple models). In the text of your findings section, you should present the standardized slope (beta) along with the t-test and the corresponding significance level. Social researchers also report the percentage of variance explained (r^{2)} along with the corresponding F test. Cronk (2012) suggests the following format for reporting regression findings:

- A multiple linear regression was calculated to predict DV based on IV1 and IV2
- A significant regression equation was found F(df regression, df residual) =F, p= sig, with an r2 of ___
- Respondents predicted that DV = constant coefficient +IV1 coefficient + IV2 Coefficient
- Interpret the meaning of the IV coefficients
- State if the IVs are statistically significant (see the coefficient sig)
- If the regression model contains many variables, you need to report on the overall fit of the model.

Here is an example:

A multiple linear regression was calculated to predict grades in SOCI 200 and age. A significant regression equation was found: age significantly predicted grades in SOCI 200, b = -.14, t(152) = 10.53, p < .001. Age also explained a significant proportion of variance in SOCI 200 grades, r^{2}= .36 or 36% of variation in SOCI 200 grades.

You should also report on regression equation using the following formula

Y =intercept +b (Independent variables),

where Y is the dependent variable and b are the beta coefficients of the independent variables

E.g., Predicted Sociology 222 Grades = intercept + (−.14)*Age

## Logistic Regression

Unlike linear regression where the outcome variable is continuous, with logistic regression, the outcome variable is binary. However, like linear regression, the results of logistic regressions are generally reported in tabular formats, with the independent variables in the rows and the following statistics in the column: beta coefficient (b), standard error (s.e), Wald’s X^{2} , degree of freedom (df), p value and odds ratio (eβ). In the text of your paper, you should comment on an overall evaluation of the logistic model; provide statistical tests of individual predictors; highlight goodness-of-fit statistics and provide an assessment of the predicted probabilities (Peng et al, 2002). You should also present the regression equation including the Y-intercept. Your write up could look like the below:

A logistic regression was performed to ascertain the effects of age, education, study status, residential status and gender on the likelihood that students pass or fail SOCI 200. The logistic regression model was statistically significant, X2 (6, N = 200) = 24.53, p = .002. The model explained 33.0% (Nagelkerke r^{2}) of the variance SOCI 200 grades and correctly classified 73.0% of cases.

Next, discuss the odds ratio for the Independent variables and confidence interval. For example:

Students aged 20 years and younger were twice as likely to pass Sociology 222 than students aged 21 years and older (OR=2.02, 95%CI [1.7, 2.5]).

Let us assume that age, study status and gender are statistically significant and the corresponding betas are -0.0261, 0.477 and -.0361 respectively, and the y-intercept is .5340. The logistic regression equation would be written similar to a linear regression equation, i.e.,

Y =intercept +b (Independent variables)

Predicted logit of (Sociology 222 Grades) = 0.5340 + (−0.0261)*Age + (0.477)*study status +(-0.0361 gender)

For a summary of reporting logistic regression in your paper, see Peng et al (2002.

# Additional Resources

**Research Commons Resources for Logistic Regressions**

Remember to visit UBC Research Commons for tutorials on how to generate and interpret logistic regressions and other procedures in SPSS https://researchcommons.library.ubc.ca/introduction-to-spss-for-statistical-analysis/

# References

Cronk, B. C. (2012). *How to use SPSS statistics: A step-by-step guide to analysis and interpretation*. Pyrczak Pub.

Peng, C. Y. J., Lee, K. L., & Ingersoll, G. M. (2002). An introduction to logistic regression analysis and reporting. *The journal of educational research*, 96(1), 3-14.