Final answer:
Outliers in data can be identified using graphical methods, by drawing lines that are two standard deviations away from the best-fit line, or numerically, by comparing the residuals to twice the standard deviation, or through the IQR method. One must decide whether to remove an outlier based on its cause and impact on the study.
Step-by-step explanation:
Identifying Outliers in Data
To determine whether there are outliers in a set of data, you can use both graphical and numerical methods. Graphically, on a scatter plot, you can draw lines that are two standard deviations above and below the best-fit line. Data points beyond these lines are potential outliers. Numerically, calculate each residual and compare it to twice the standard deviation of the residuals. If a point's residual exceeds this value, it is considered an outlier.
Numerical Method Using IQR
For the numerical method involving the interquartile range (IQR), calculate the IQR (Q3 - Q1) and then find the upper and lower bounds by calculating Q1 - 1.5*IQR and Q3 + 1.5*IQR, respectively. Any data points outside these bounds are classified as outliers.
Handling Outliers
After identifying an outlier, it's important to assess whether it should be removed. This depends on whether the outlier is a result of an error or is a valid observation that can influence the study's findings. Removing an outlier should lead to a new line with a smaller SSE (sum of the squared errors) and a correlation coefficient closer to 1 or -1, indicating a better fit.