Assumptions of simple linear regression
Simple linear regression is a parametric test, meaning that it makes certain assumptions about the data. These assumptions are:
Linear regression makes one additional assumption:
4.The relationship between the independent and dependent variable is linear: the line of best fit through the data points is a straight line (rather than a curve or some sort of grouping factor).
Linearity: The relationship between and must be linear.
Check this assumption by examining a scatterplot of x and y.
Independence of errors: There is not a relationship between the residuals and thevariable; in other words, is independent of errors.
Check this assumption by examining a scatterplot of “residuals versus fits”; the correlation should be approximately 0. In other words, there should not look like there is a relationship.
Normality of errors: The residuals must be approximately normally distributed.
Check this assumption by examining a normal probability plot; the observations should be near the line. You can also examine a histogram of the residuals; it should be approximately normally distributed.
Equal variances: The variance of the residuals is the same for all values of.
Check this assumption by examining the scatterplot of “residuals versus fits”; the variance of the residuals should be the same across all values of the x-axis. If the plot shows a pattern (e.g., bowtie or megaphone shape), then variances are not consistent, and this assumption has not been met.
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