Section 10.4 Assumptions of Linear Regression
In the previous chapter, I emphasized the importance of checking multiple assumptions when conducting statistical analyses, as violating these assumptions can significantly impact linear regression results and lead to biased estimates of coefficients. To ensure the validity of our analysis, we need to consider several additional assumptions. Some of these may already be familiar to you, as they were also necessary for correlation analysis.
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Each observation in our dataset should be independent of the others.
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The outcome variable we are analyzing should be continuous.
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The relationship between the outcome variable and each continuous predictor should be linear.
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The variance of the outcome variable should be constant across all levels of the predictors, with points evenly distributed around the regression line.
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The residuals (the differences between observed and predicted values) should be independent of each other.
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The residuals should follow a normal distribution.
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There should be no strong correlations among the predictor variables, as this can cause numerical instability in the estimation of coefficients.
There are various methods available in R to assess these assumptions. However, discussing them in detail would exceed the scope of our current analysis. For the purposes of demonstration, we will proceed with the analysis, assuming that these assumptions have been met.
