SIMPLE REGRESSION
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Using Linear Regression test in Research
This easy tutorial will show you how to run Simple Regression Analysis test in SPSS, and how to interpret the result.
Regression analysis is a parametric technique that we can use to examine the relationship between two variables, one dependent and one independent. Firstly, The value of the dependent variable is estimated based on the value of the independent variable. Secondly, the dependent variable is usually denoted by Y, and the independent variable by X. Certainly, the regression equation takes the following form:
where y is a dependent variable, is intercept, is the slope of the regression line, x is the independent variable, and is error term.
Regression analysis is a type of statistical evaluation that enables three things:
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Description: Relationships among the dependent variables and we can describe the independent variables as a means of regression analysis.
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Estimation: We can estimate the values of the dependent variables from the observed values of the independent variables.
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Prognostication: We can identifi the risk factors as an influence the outcome, and we can determined the individual prognoses. (Source)
Assumptions of the Regrression Analysis Test:
Assumptions for simple regression:
- continuous dependent variable
- continuous or dichotomous (1 or 0, dummy variable) independent variable
- normal distribution of data
- no autocorrelation
An Example: Simple Regression Test
This guide will explain, step by step, how to run a Simple Regression Test in SPSS statistical software by using an example.
Firstly, We collected data from students about their level of happiness with their life and level of depression. Moreover, happiness was rated on a scale of 1 to 2, while depression was rated on a scale of 1 to 10. As a result, we wanted to examine how the level of depression predicts the level of happiness.
This easy tutorial will show you how to run a Simple Regression Test in SPSS, and how to interpret the result.
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How to Run Regression Analysis in SPSS: Explanation Step by Step
From SPSS menu, choose Analyze – Regression – Linear
A new window will open.
We want to examine whether the level of depression predicts the level of happiness, our dependent variable is Happiness, and our independent variable is Depression. Therefore, from the left box, we will transfer variable Happiness into the Dependent box and variable Depression into Independent(s) box.
Click on the Statistics tab and open a new window.
In the box, Regression Coefficients check Estimates, Confidence intervals. In the box Residuals check Durbin-Watson. Also check Model fit, Descriptives, Collinearity diagnostics. Click Continue.
Click on the Plots tab to show scatterplot for residuals.
From the left box transfer ZRESID into Y box, and ZPRED into X box. Click Continue and OK.
The results will appear in the output window.
How to report Linear Regression Analysis results: Explanation Step by Step
How to Report Descriptive Statistics Table in SPSS Output?
The first table in the output window shows descriptive statistics (mean, standard deviation, and number of observations) for our variables: Happiness and Depression.
How to Report Correlation Table in SPSS Output?
The second table shows the correlation between Happiness and Depression.
Pearson correlation coefficient shows statistically significant and negative relationship between level of happiness and level of depression, [r(59) = -.291, p = .013]. As the level of depression increases, the level of happiness decreases.
How to Report Variable Table SPSS Output?
The next table from the output shows which variables we used (dependent and independent) and method (Enter).
How to Report Model summary in SPSS output?
The next table shows the Model summary.
R-square shows what percent of the variance in the dependent variable is explained by independent variables. In our example, R2 = .085 indicates that just 8.50% of the variance in the level of happiness is explained by the level of depression.
Durbin-Watson statistic shows whether there is autocorrelation in the model. That is to say, According to Field (2009), values from 1 to 3 are acceptable for DW statistics, and there is no autocorrelation.
How to Report ANOVA table for Regression Analysis in SPSS Output?
The next table shows the ANOVA results.
How to Report Regression Analysis Result in SPSS Output?
The next table shows the Regression analysis results.
Firstly, we should look at whether is our independent variable statistically significant. So, we look column Sig. and the second row (Depression)
If the p-value is greater than 0.05. Therefore, the independent variable (depression) does not significantly predict the dependent variable (happiness).
In our example, the p-value is 0.025 and lower than 0.05. So, depression does significantly predict happiness.
Secondly, the sign of unstandardized coefficient B for the independent variable is positive. Therefore, we can say that the independent variable positively predicts the dependent variable. Likewise, if the independent variable increases for one unit, the dependent variable will increase for B units.
For example, unstandardized coefficient B for depression is negative. So, we can say that level of depression negatively predicts the level of happiness. Consequently, if the level of depression increases for one unit, the level of happiness will decrease by .128 units.
A regression analysis was computed to determine whether the level of depression predicts the level of happiness in a sample of 59 students (N = 59). Firstly, the results of the coefficient indicate a significant negative relationship between the variables, [r(59) = -.291, p = .013].
Therefore, the equation for the regression line is the level of happiness = b0 + b1*level of depression. To clarify, the confidence interval of the slope ranged from -.240 to -.017, an interval that does not contain the value of 0. R2 = .085 indicates that just 8.50% of the variance in the level of happiness is explained by the level of depression.
The results of ANOVA were significant, F(1, 57) = 5.29, p = .025.
Therefore, we reject the null hypothesis that the slope of our regression line is 0 and conclude that the level of depression does significantly predict the level of depression. Consequently, If the level of depression increases for one unit, the level of happiness will decrease by .128 units.
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