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Regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome variable') and one or more independent variables (often called 'predictors', 'covariates', or 'features').
The most common form of regression analysis is linear regression, in which a researcher finds the line (or a more complex linear combination) that most closely fits the data according to a specific mathematical criterion.
In short, regression analysis...
Measures the effect of IV(s) on a DV.
Assesses the contribution of IV(s) to a DV.
Examines amount of variance in the DV, which is explained by IV(s)
Multiple Linear Regression Analysis
Multiple Linear Regression Analysis
Multiple regression analysis is a statistical technique that can be used to analyze the relationship between a single dependent variable (continuous) and several independent variables (continuous or even nominal).
Multiple linear regression analysis can be used in 3 different situations.
To develop an equation that can be used to predict the value of a dependent variable (Y) if given values of several independent variables (X).
To control for confounding variables so that we can evaluate the contribution of the variables that we would like to study. This is usually called statistical control.
To test and explain causal theories which are also commonly termed as path analysis. The linkages among construct must be guided by a theory before they can be considered causal.
The most common way of depicting the regression is shown below.
Y = a + b1X1 + b2X2 + b3X3 + e
Where,
Y = dependent variable
a = intercept
b1, b2 b3 = regression coefficients (slope)
X1, X2, X3 = independent variables
e = random error
Standardized regression betas are also called beta weights and their values indicate the relative importance of the independent variable.
Things to Consider
Things to Consider
Strong theory (conceptual or theoretical): When developing a regression model there should be a strong theory that should guide the modelling, or else the model may not work the way we wanted it to.
Measurement error: It is the degree to which the variable is an accurate and consistent measure of the concept being studied. If the error is high, than even the best predictors may not be able to achieve sufficient predictive accuracy.
Specification error: It is the inclusion of irrelevant variables or omission of relevant variables from the set of independent variables.
Multiple Linear Regression in SPSS
Multiple Linear Regression in SPSS
Step 1: Select Analyze, Regression, Linear.
Step 2: Select 1 dependent variable and move them move them to the Dependent box. Select dependent variable(s) and move them to Independent(s) box.
Method is enter: This method is where all the variables are included to see which variables are significant and which are not.
Step 3: Click Statistics, and select the required statistics. Continue.
Step 4: Click Plots, select the required plots. Continue and OK.
Critical t-values
Critical t-values
If t-value is greater than or equal to 1.645, then the relationship is significant at alpha < 0.05 (1-tailed test).
Coefficients of determination (R-square)
Coefficients of determination (R-square)
R-square indicates the contribution of independent variables on a dependent variable. It shows how much the variances in the dependent variable are determined by the independent variables.
Examples of Reporting Style
Examples of Reporting Style
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