Stata Tutorial - Data and Statistical Services - Princeton University

Goal: run a multiple linear regression model.9. Obtain linear regression estimatesTyping commands in the Command windowIn estimating relationships among variables, you mayfirst want to examine how the variables are correlated.We suspect that MPG and WEIGHT are correlated.Let’s see the correlation:. correlate mpg weightIn addition, we suspect that the correlation may bedifferent between foreign and domestic cars. We cancombine the –correlate- command with a by statement.Before using a by statement, the data need to be sortedby the by-variable.. sort foreign. by foreign: correlate mpg weightIt seems that mpg and weight have a relatively highcorrelation. The correlation is different for foreign anddomestic cars, so foreign must also impact MPG.From the scatterplots we saw earlier, we also discoveredthat the relationship between WEIGHT and MPG isnot exactly linear. We’ll include a square of WEIGHTto improve the model. Let’s run a regression estimatingMPG by WEIGHT, WEIGHT2 and FOREIGN.. regress mpg weight weight2 foreignAfter estimating a regression model, we can use thevalues estimated by the model, called post-estimationvalues. Using estimated MPG, we can see how theestimated line fit the original distribution by viewingoverlaid graph. To do so, we first need to create avariable for the predicted MPG. We’ll call thisMPGHAT.. predict mpghat. graph twoway (scatter mpg weight) (line mpghatweight), by (foreign)Review Questions:1. What is the correlation between MPG andWEIGHT?2. Is the correlation different between domesticand foreign cars?3. How do I obtain regression estimates?4. How can I compare observed and predictedvalues on a graph?using MenusStatistics=> Summaries, tables,and tests=> Summary anddescriptive statistics=>Correlations and covariancesData=> Sort=> Ascending sortStatistics=> Summaries, tables,and tests=> Summary anddescriptive statistics=>Correlations and covariances, in“by/if/in” tab click Repeatcommand by groups, insertforeign in Variables that definegroups:Statistics=> Linear models andrelated=> Linear regressionStatistics=> Postestimation=>Predictions, residuals, etc.,Graphics=> Two-way graph(if there are already definedplots in “Plot definitions:”, eitherDisable or Edit them to createnew combinations)Notes and Tips. pwcorr mpg weight, star(.05)adds an asterisc (*) next to thecorrelation coefficients that arestatistically significat at 95% level.You can also sort and use “bystatement” in one step:. bysort foreign: correlate mpg weightThere are series of regressiondiagnostics you can do using graphs.See UCLA’s Stata tutorial site formore information.To compute a square of WEIGHT,WEIGHT2, you can multiply WEIGHTby itself, or raise it to the power of 2.. generate weight2 = weight*weight. generate weight2 = weight^2do the same thing.Stata has a series of “post estimationcommands.” After running aregression estimates, for example,you can test if the coefficients arestatistically significantly different from0, or from another independentvariable (wald test), or test forheteroscedasticity. For details, see. help regress postestimation,xb that appear as an option whenmenu is used is a default incommand window input. It will notappear in the Results window whencommand is input in the Commandwindow.Hints:. correlate. by varname: correlate. regress. predict yhat. graph two way (scatter y x) (lineyhat x)Page 24 of 28