Regression is a complex statistical technique that tries to predict the value of an outcome or dependent variable, such as annual income, economic output or student test scores, based on one or more predictor variables, such as years of experience, national unemployment rates or student course grades. Researchers in education and social sciences use regression to study a wide range of phenomena, using statistical software programs such as SPSS to conduct their analyses. SPSS generates regression output that may appear intimidating to beginners, but a sound understanding of regression procedures and an understanding of what to look for can help the student or novice researcher interpret the results.
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Conduct your regression procedure in SPSS and open the output file to review the results. The output file will appear on your screen, usually with the file name "Output 1." Print this file and highlight important sections and make handwritten notes as you review the results.
Begin your interpretation by examining the "Descriptive Statistics" table. This table often appears first in your output, depending on your version of SPSS. The descriptive statistics will give you the values of the means and standard deviations of the variables in your regression model. For example, a regression that studies the effect of years of education and years of experience on average annual income will have the means and standard deviations in your data for these three variables.
Turn your attention to the correlations table, which follows the descriptive statistics. Correlations will measure the degree to which these variables are related. Correlations range in value from zero to one. The higher the value, the greater the level of correlation. The values can be positive or negative, signifying positive or negative correlation.
Review the model summary, paying particular attention to the value of R-square. This statistic tells you how much of the variation in the value of the dependent variable is explained by your regression model. For example, regressing average income on years of education and years of experience may produce an R-square of 0.36, which indicates that 36 per cent of the variation in average incomes can be explained by variability in a person's education and experience.
Determine the linear relationship among the variables in your regression by examining the Analysis of Variance (ANOVA) table in your SPSS output. Note the value of the F statistic and its significance level (denoted by the value of "Sig."). If the value of F is statistically significant at a level of 0.05 or less, this suggests a linear relationship among the variables. Statistical significance at a .05 level means there is a 95 per cent chance that the relationship among the variables is not due to chance. This has become the accepted significance level in most research fields.
Study the coefficients table to determine the value of the constant. This table summarises the results of your regression equation. Column B in the table gives the values of your regression coefficients and the constant, which is the expected value of the dependent variable when the values of the independent variables equal zero.
Study the values of the independent variables in the coefficients table. The values in column B represent the extent to which the value of that independent variable contributes to the value of the dependent variable. For example, a B of 800 for years of education suggests that each additional year of education raises average income by an average of £520 a year. The t-values in the coefficients table indicate the variable's statistical significance. In general, a t-value of 2 or higher indicates statistical significance.
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