Linear Regression using Stata

Explore how multiple linear regression extends simple regression by incorporating attendance and study to predict GPA.

Explore how multiple linear regression uses attendance and study to predict GPA, interpret coefficients, and compare effects, showing attendance has a larger impact than study.

Use r-squared to compare models; adding attendance and study raises r-squared from 0.75 to 0.90, showing the multiple linear regression better explains GPA variation.

Explore how p-values indicate statistical significance in a multiple linear regression, with each coefficient's p-value below 0.05 signaling significance and justifying including attendance and study in the model.

Assess fit and residuals in a regression predicting GPA from attendance and study in Stata, noting r-squared and p-values; interpret residuals as observed minus predicted and aim for small residuals.

Learn how to encode a binary variable, like gender, as 0/1 for linear regression, interpret coefficients, and compare reference categories in a multiple regression.

Learn how to code categorical variables in linear regression using dummy variables, with a four-group major example, where coefficients compare each group to the reference (business).

Explore quadratic terms in linear regression by adding an English squared predictor to model non-linear GPA relationships, showing improved r-squared and significant p-values for both terms.

After fitting the linear regression model, assess fit and assumptions by comparing predicted to observed GPA and visualize fitted versus observed values to see alignment near the y=x line.

Examine the normality of residuals in linear regression by plotting a histogram and overlaying a normal curve, and assess independence and constant variance to validate model assumptions.

Test independence by plotting residuals against fitted values or independent variables to check for patterns. A random scatter indicates independence; a pattern such as a U shape signals dependence.

Assess residuals to verify the constant variance assumption in linear regression with Stata by plotting against x or fitted values, highlighting any growing spread.

Assess multicollinearity in multiple linear regression by computing variance inflation factors (VIF) for each independent variable; if any VIF exceeds 10, remove that variable.

Identify and diagnose outliers in linear regression using diagnostics to assess model fit, understand influential observations, and compare regression lines with and without outliers.

Identify influential observations in linear regression by evaluating how results change when each data point is removed, using three influence statistics, illustrated with a GPA and attendance example.

Explore forward selection, backward elimination, and stepwise regression to choose among multiple independent variables, and compare models using adjusted r squared, prioritizing literature-informed decisions over algorithm-only choices.

Explore how to apply linear regression with Stata, read output, and perform diagnostics and assumption checks using intuitive commands.

Explore simple linear regression with Stata by loading a dataset, plotting a scatter plot of GPA against attendance, and interpreting the regression output: GPA equals 1.22 times attendance minus 13.2.

predict GPA values from the regression model and compare GPA_predicted to observed GPA to assess model fit, then evaluate residuals with histogram and a Q normal plot, noting nonnormality.

In this Stata multiple linear regression, GPA is modeled with attendance and study hours as predictors; GPA = 0.71 attendance + 0.59 study + 6.98, with attendance a larger effect.

Assess model fit by comparing simple and multiple regression using adjusted r-squared and p-values, then predict GPA and examine residuals with histograms and q-q plots for normality.

Learn to include a binary gender variable in linear regression with Stata, using i. and B1 to set reference groups, interpreting a 4.29 GPA difference and improved adjusted R-squared.

Encode a multi-category variable with i.major in regression, compare each group (engineering, biology, philosophy) to a business reference, and switch the base group with B to change the baseline.

Explore how a quadratic term for English improves GPA regression in Stata, using either English squared or an English-by-English interaction, indicating a nonlinear relationship with significant results (p<0.05).

Learn how to assess model fit and assumptions in a multiple linear regression predicting GPA from attendance and gender, using predicted vs observed plots, adjusted r-squared, and p-values.

Calculate residuals with the predict command, then use the q normal command to visualize, and apply the Shapiro-Wilk and another normality test to confirm residuals are normally distributed.

Assess independence of residuals and constant variance in linear regression by plotting residuals against fitted values, using a zero line, and applying Stata's robust standard errors when needed.

Run a regression in Stata, then use the vif command to compute VIF values for each independent variable. All VIFs are below 10, indicating no multicollinearity.

Identify and diagnose outliers in simple and multiple linear regression using diagnostic plots, av plots and leverage-residuals plots, and assess their influence on model results.

Identify and assess influential observations using Cook's distance and dfits in Stata; create new influence variables, predict fits, and visualize influential points to decide whether to exclude problematic cases.

Explore selection algorithms in Stata: forward selection and backward elimination identify best predictors for GPA. Stepwise with p<0.05 selects English and attendance as the final model, aligning with dataset insights.

Learn to visualize regression results in Stata using margins plot and margins after analysis, and customize graphs that clearly summarize each independent variable's effect on the dependent variable.

Explore how to visualize effects in multiple linear regression using Stata by applying the margins and margins plot commands to predict GPA across attendance values 40 to 100.

Explore a multiple linear regression with attendance and a gender indicator, using margins and margin plots to compare GPA by gender, showing females score higher than males across attendance levels.

Explore three-variable regression with continuous attendance and study hours plus a categorical gender predictor, using margins and margins plot in stata to visualize predicted gpa across values.

Explore how using interaction terms instead of squared predictors clarifies nonlinear relationships in linear regression, visualize with margins plots, and interpret results using Stata.

Explore a dataset with more than 800 observations to apply multiple linear regression in Stata, including scatter plots, predicting gpa with residuals, model comparison by adjusted r-squared, and testing assumptions.

Explore a large Stata dataset to model GPA with linear regression, examining variables like college, credits, gender, attendance, English, siblings, income, and work, and test model fit and assumptions.

Review the core theory, learn to analyze data sets and statistics, and apply a solo project in linear regression using Stata.