Visualizing Linear Regression: How to Plot Fitted Lines and Confidence Intervals in Stata скачать в хорошем качестве

Visualizing Linear Regression: How to Plot Fitted Lines and Confidence Intervals in Stata

The Stata command twoway lfitci is an essential graphical tool for applied econometrics, designed to visualize the linear relationship between a dependent variable (y) and an independent variable (x). It calculates the prediction for y based on a linear regression on x and plots the resulting fitted line accompanied by a confidence interval (CI). By default, the command computes and displays a 95% confidence interval for the predicted mean, typically rendered as a shaded region (rarea) surrounding the regression line. To execute this in Stata, the basic syntax is twoway lfitci yvar xvar. The command offers flexibility for specific analytical needs. For instance, adding the stdf option calculates the CI based on the standard error of the forecast (individual prediction) rather than the mean, which includes uncertainty from both the mean prediction and the residual. This feature is particularly useful for identifying outliers in the data. The confidence level can also be adjusted using level(#), such as level(99). Visually, the CI appearance can be altered from a shaded area to bounding lines using ciplot(rline) or customized further with pattern options like blpattern(dash). In practice, lfitci is frequently overlayed with a scatterplot to visually assess how well the linear model fits the observed data points. Users can combine plots using the pipe operator, as seen in the syntax twoway lfitci y x || scatter y x. However, researchers must avoid using this command when specifying logarithmic axis scales (e.g., xscale(log)), as the prediction line will not render correctly as a straight line. The Difference Between stdp and stdf in Confidence Interval Plotting In Stata's twoway lfitci command, the distinction between the options stdp and stdf lies in the specific type of uncertainty incorporated into the confidence interval (CI). By default, the command uses stdp, which calculates the CI based on the standard error of the prediction. This interval represents the confidence interval of the mean, reflecting the precision with which the regression line estimates the average value of the dependent variable for a given predictor. Conversely, the stdf option calculates the CI based on the standard error of the forecast. This interval applies to an individual prediction rather than the population mean. Crucially, stdf accounts for a broader scope of uncertainty: it includes both the uncertainty associated with the mean prediction (as found in stdp) and the uncertainty derived from the residual (the random error term of a specific observation). Consequently, the intervals generated by stdf are wider than those produced by stdp because they must encompass the natural variability of individual data points in addition to the uncertainty of the model parameters. Practically, while stdp is standard for visualizing the fit of the regression line, stdf is particularly valuable for outlier detection. If an observed data point falls outside the wider CI generated by stdf, it indicates that the specific observation is unlikely given the model's forecast.