Results showed that there was a statistically significant relationship between the explanatory variables hours and hours 2 and the response variable happiness (F(2, 13) = 65.095, p < 0.000).Ĭombined, these two explanatory variables accounted for 90.9% of variability in happiness.Įstimated happiness level = -30.253 + 7.173(hours) –. A sample of 16 individuals was used in the analysis.
#QUADRATIC REGRESSION HOW TO#
Here is an example of how to do so:Ī quadratic regression was performed to quantify the relationship between the number of hours worked by an individual and their corresponding happiness level (measured from 0 to 100). Lastly, we want to report the results of our quadratic regression. 107*(60 2) = 14.97.Ĭonversely, an individual that works 30 hours perk week is predicted to have a happiness level of 88.65:Įstimated happiness level = -30.253 + 7.173*(30) –. For example, an individual that works 60 hours per week is expected to have a happiness level of 14.97:Įstimated happiness level = -30.253 + 7.173*(60) –. We can use this equation to find the estimated happiness level for an individual based on the number of hours they work per week. We can use the values in the column Unstandardized B to form the estimated regression equation for this dataset:Įstimated happiness level = -30.253 + 7.173*(hours) –. The next table we’re interested in is titled Coefficients: In this case the p-value is equal to 0.000, which indicates that the explanatory variables hours and hours 2 combined have a statistically significant association with exam score. It tells us whether or not the regression model as a whole is statistically significant.
The next table we’re interested in is titled ANOVA: In this example, the observed values fall an average of 9.519 units from the regression line.
Error of the Estimate: The standard error is the average distance that the observed values fall from the regression line. In this example, 90.9% of the variation in happiness can be explained by the variables hours and hours 2. R Square: This is the proportion of the variance in the response variable that can be explained by the explanatory variables.Here is how to interpret the most relevant numbers in this table: The first table we’re interested in is titled Model Summary: Once you click OK, the results of the quadratic regression will appear in a new window. Drag hours and hours2 into the box labeled Independent(s). In the new window that pops up, drag happiness into the boxed labeled Dependent. Click on the Analyze tab, then Regression, then Linear: Next, we will perform quadratic regression. Once you click OK, the variable hours2 will appear in a new column: In the new window that pops up, name the target variable hours2 and define it as hours*hours: This tells us that quadratic regression is an appropriate technique to use in this situation.īefore we can perform quadratic regression, we need to create a predictor variable for hours 2.Ĭlick the Transform tab, then Compute variable: We can clearly see that a non-linear relationship exists between hours worked and happiness. Drag the variable hours onto the x-axis and happiness onto the y-axis. Then drag the chart titled Simple Scatter into the main editing window. In the new window that pops up, choose Scatter/Dot in the Choose from list. Use the following steps to perform a quadratic regression in SPSS.īefore we perform quadratic regression, let’s make a scatterplot to visualize the relationship between hours worked and happiness to verify that the two variables actually have a quadratic relationship.Ĭlick the Graphs tab, then Chart Builder: We have the following data on the number of hours worked per week and the reported happiness level (on a scale of 0-100) for 16 different people: Suppose we are interested in understanding the relationship between number of hours worked and happiness. This tutorial explains how to perform quadratic regression in SPSS. In these cases, you can try using quadratic regression. However, simple linear regression doesn’t work well when two variables have a non-linear relationship. When two variables have a linear relationship, you can often use simple linear regression to quantify their relationship.
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