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Simple Linear RegressionSimple Linear Regression establishes the relationship between two variables using a straight line. It attempts to draw a line that comes closest to the data by finding the slope and intercept which define the line and minimize regression errors. Simple linear regression has only one x and one y variable. Multi Linear RegressionMultiple Linear regressions are based on the assumption that there is a linear relationship between both the dependent and independent variables or Predictor variable and Target variable. It also assumes that there is no major correlation between the independent variables. Multi Linear regressions can be linear and nonlinear. It has one y and two or more x variables or one dependent variable and two or more independent variables. Polynomial RegressionY=θo + θ₁X + θ₂X² + … + θₘXᵐ + residual error Polynomial Regression is a one of the types of linear regression in which the relationship between the independent variable x and dependent variable y is modeled as an nth degree polynomial. Polynomial regression fits a nonlinear relationship between the value of x and the corresponding conditional mean of y, denoted E (y |x). Polynomial Regression provides the best approximation of the relationship between the dependent and independent variable. At the end of this section you should be able to answer the following questions:
Multiple Regression is a step beyond simple regression. The main difference between simple and multiple regression is that multiple regression includes two or more independent variables – sometimes called predictor variables – in the model, rather than just one. As such, the purpose of multiple regression is to determine the utility of a set of predictor variables for predicting an outcome, which is generally some important event or behaviour. This outcome can be designated as the outcome variable, the dependent variable, or the criterion variable. For example, you might hypothesise that the need to belong will predict motivations for Facebook use and that self-esteem and meaningful existence will uniquely predict motivations for Facebook use. Before beginning your analysis, you should consider the following points:
Please click on the link labeled “Venn Diagrams” to work through an example.
In these Venn Diagrams, you can see why it is best for the predictors to be strongly correlated with the dependent variable but uncorrelated with the other Independent Variables. This reduces the amount of shared variance between the independent variables. The illustration in Slide 2 shows logical relationships between predictors, for two different possible regression models in separate Venn diagrams. On the left, you can see three partially correlated independent variables on a single dependent variable. The three partially correlated independent variables are physical health, mental health, and spiritual health and the dependent variable is life satisfaction. On the right, you have three highly correlated independent variables (e.g., BMI, blood pressure, heart rate) on the dependent variable of life satisfaction. The model on the left would have some use in discovering the associations between those variables, however, the model on the right would not be useful, as all three of the independent variables are basically measuring the same thing and are mostly accounting for the same variability in the dependent variable. There are two main types of regression with multiple independent variables:
We will now be exploring the single step multiple regression: All predictors enter the regression equation at once. Each predictor is treated as if it had been analysed in the regression model after all other predictors had been analysed. These predictors are evaluated by the shared variance (i.e., level of prediction) shared between the dependant variable and the individual predictor variable. Multiple Regression AssumptionsThere are a number of assumptions that should be assessed before performing a multiple regression analysis:
Multiple Regression InterpretationFor our example research question, we will be looking at the combined effect of three predictor variables – perceived life stress, location, and age – on the outcome variable of physical health? Please open the output at the link labeled “Chapter Five – Standard Regression” to view the output.
Slide 1 contains the standard regression analysis output. On Slide 2 you can see in the red circle, the test statistics are significant. The F-statistic examines the overall significance of the model, and shows if your predictors as a group provide a better fit to the data than no predictor variables, which they do in this example. The R2 values are shown in the green circle. The R2 value shows the total amount of variance accounted for in the criterion by the predictors, and the adjusted R2 is the estimated value of R2 in the population. Moving on to the individual variable effects on Slide 3, you can see the significance of the contribution of individual predictors in light blue. The unstandardized slope or the B value is shown in red, which represents the change caused by the variable (e.g., increasing 1 unit of perceived stress will raise physical illness by .40). Finally, you can see the standardised slope value in green, which are also known as beta values. These values are standardised ranging from +/-0 to 1, similar to an r value. We should also briefly discuss dummy variables: A dummy variable is a variable that is used to represent categorical information relating to the participants in a study. This could include gender, location, race, age groups, and you get the idea. Dummy variables are most often represented as dichotomous variables (they only have two values). When performing a regression, it is easier for interpretation if the values for the dummy variable is set to 0 or 1. 1 usually resents when a characteristic is present. For example, a question asking the participants “Do you have a drivers license” with a forced choice response of yes or no. In this example on Slide 3 and circled in red, the variable is gender with male = 0, and female = 1. A positive Beta (B) means an association with 1, whereas a negative beta means an association with 0. In this case, being female was associated with greater levels of physical illness. Multiple Regression Write UpHere is an example of how to write up the results of a standard multiple regression analysis: In order to test the research question, a multiple regression was conducted, with age, gender (0 = male, 1 = female), and perceived life stress as the predictors, with levels of physical illness as the dependent variable. Overall, the results showed the utility of the predictive model was significant, F(3,363) = 39.61, R2 = .25, p< .001. All of the predictors explain a large amount of the variance between the variables (25%). The results showed that perceived stress and gender of participants were significant positive predictors of physical illness (β=.47, t= 9.96, p< .001, and β=.15, t= 3.23, p= .001, respectively). The results showed that age (β=-.02, t= -0.49 p= .63) was not a significant predictor of perceived stress. What is the difference between simple regression and multiple regressions?Multiple Regression is a step beyond simple regression. The main difference between simple and multiple regression is that multiple regression includes two or more independent variables – sometimes called predictor variables – in the model, rather than just one.
What is the difference between simple and multiple regression quizlet?What is the difference between simple linear regression and multiple regression? Simple linear regression has one independent variable and multiple regression has two or more.
What is the main difference between regression Analyses and simple correlation?Regression is primarily used to build models/equations to predict a key response, Y, from a set of predictor (X) variables. Correlation is primarily used to quickly and concisely summarize the direction and strength of the relationships between a set of 2 or more numeric variables.
What is the difference between multiple regression and multivariate regression?To summarise multiple refers to more than one predictor variables but multivariate refers to more than one dependent variables.
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What is the main difference between simple regression and multiple regression?
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