Correlation in Linear Regression by using Stata

Ordinary least-squares (OLS) regression finds the best-fitting straight line. A Pearson product- moment correlation coefficient describes how well the best-fitting line fits. correlate obtains correlations for listed variables. . correlate gdp school adfert chldmort life correlate reports correlations based only on those observations that have non-missing values on all of the listed variables. From

Multiple Regression by using Stata

Simple regression and correlation establish that a country’s life expectancy is related to the mean years of schooling: school by itself explains about 52% of the variance of life. But might that relationship be spurious, occurring just because both schooling and life expectancy reflect a country’s economic wealth? Does schooling matter once we control

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Hypothesis Tests with Linear Regression by using Stata

Two types ofhypothesis tests appear in regress output tables. As with other common hypothesis tests, they begin from the assumption that observations in the sample at hand were drawn randomly and independently from an infinitely large population. Overall F test: The F statistic at the upper right in the regression table evaluates the null

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Dummy Variables in Linear Regression by using Stata

Categorical variables can become predictors in a regression when they are expressed as one or more {0,1} dichotomies called dummy variables. For example, we have already seen large regional differences in life expectancies (Figure 7.1). The categorical variable region takes values from 1 (Africa) to 5 (Oceania) which can be re-expressed as a set

Interaction Effects in Linear Regression by using Stata

The previous section described what are called “intercept dummy variables,” because their coefficients amount to shifts in a regression equation’s y intercept, comparing the 0 and 1 groups. Another use for dummy variables is to form interaction terms called “slope dummy variables” by multiplying a dummy times a measurement variable. In this section we

Robust Estimates of Variance in Linear Regression by using Stata

The standard errors and hypothesis tests that accompany ordinary regression (such as regress or anova) assume that errors follow independent and identical distributions. If this assumption is untrue, those standard errors probably will understate the true sample-to-sample variation, and yield unrealistically narrow confidence intervals or too-low test probabilities. To cope with a common problem

Predicted Values and Residuals in Linear Regression by using Stata

After any regression, the predict command can obtain not only predicted values, but also residuals and other post-estimation case statistics — statistics that have separate values for each observation in the data. Switching to a different example for this section, we will look at the simple regression of September Arctic sea ice area on

Other Case Statistics with Linear Regression by using Stata

predict can also calculate many other case statistics appropriate for the recently-fitted model. After regress (or anova), predict options include the following. Substitute any new variable name for new in these examples. . predict new   Predicted values of y. predict new, xb means the same thing (referring to Xb, the vector of predicted y

Diagnosing Multicollinearity and Heteroskedasticity in Linear Regression by using Stata

Multicollinearity refers to the problem of too-strong linear relationships among the predictors or independent variables in a model. If perfect multicollinearity exists among the predictors, regression equations lack unique solutions. Stata warns us and then drops one of the offending predictors. High but not perfect multicollinearity causes more subtle problems. When we add a

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Confidence Bands in Simple Regression by using Stata

This section introduces some additional graphics that help to visualize a regression model or diagnose possible problems. Continuing with the Arctic9.dta data, variable tempN describes mean annual air temperature anomalies for the entire region from 64 to 90 degrees north latitude, estimated from land and sea surface records by NASA. Temperature anomalies represent differences,

Diagnostic Graphs with Linear Regression by using Stata

Stata offers many specialized graphs useful for diagnostic purposes following a regression. A few of these are illustrated in this section; type help regress postestimation for a list. Our example here will be an elaboration of the Arctic ice model, in which September sea ice area is predicted from year and year2 (after year

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Lowess Smoothing by using Stata

Lowess smoothing, already demonstrated without explanation at several points in this book, is a very useful tool for nonparametric regression. Nonparametric regression methods generally do not yield an explicit regression equation, and do not require the analyst to specify a relationship’s functional form in advance. Instead, they help to explore the data with an

Robust Regression by using Stata

Stata’s basic regress and anova commands perform ordinary least squares (OLS) regression. The popularity of OLS derives in part from its theoretical advantages given ideal data. If errors are normally, independently and identically distributed (normal i.i.d.), then OLS is more efficient than any other unbiased estimator. The flip side of this statement often gets

Further rreg and qreg Applications by using Stata

The previous section showed basic applications of rreg and qreg. These commands also can be used in many other ways, from simple to complex. For example, to obtain a 90% confidence interval for the mean of a single variable such as Antarctic air temperature (tempS), we could type the usual confidence-interval command ci: Alternatively,

Nonlinear Regression — part 1

Variable transformations allow fitting some curvilinear relationships using the familiar techniques of intrinsically linear models. Intrinsically nonlinear models, on the other hand, require a different class of fitting techniques. The nl command performs nonlinear regression by iterative least squares. This section illustrates with the artificial examples in nonlin.dta: The nonlin.dta data are manufactured, with

Nonlinear Regression — part 2

September ice in the Arctic (Arctic9.dta) provides a real-world example. Previously we saw that sea ice area declined over 1979-2011, the period of close satellite observation. Diagnostic graphs reveal that a linear model fits poorly, however, because the decline has been faster than linear (Figures 7.9, 7.11). An alternative quadratic model better describes the

Box–Cox Regression by using Stata

Leaving colder regions behind, the remainder of this chapter works with the United Nations human development data in Nations3.dta. Nonlinear relationships among variables are prominent in scatterplots of these data, such as that in Figure 7.4. Logarithms and other transformations from Tukey’s ladder of powers (Chapter 5) provide simple tools for making nonlinear relationships

Multiple Imputation of Missing Values in Stata

Nations3.dta contains information about 194 countries, but missing values restrict our analysis in previous sections to a subset of 178 that have complete information on all variables of interest. This listwise deletion approach of setting aside incomplete observations is, out of necessity, a common statistical practice. Its known drawbacks include loss of observations and

Structural Equation Modeling by using Stata

The regression models above treat adolescent fertility, percent urban and other national characteristics as possible predictors of life expectancy, without necessarily asserting that they are its causes. One of those predictors, child mortality rate, has an obvious causal connection with life expectancy. But child mortality rates in turn are influenced by other national characteristics

Space Shuttle Data in Stata

Our first example for this chapter, shuttle.dta, involves historical data covering the first 25 flights of the U.S. space shuttle. These data contain evidence that, if properly analyzed, might have persuaded NASA officials not to launch Challenger on its fatal flight in 1985 (the 25th shuttle flight, designated STS 51-L). The data are drawn

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