linear regression

In your typical statistical work, chances are you have already used quantiles such as the median, 25th or 75th percentiles as descriptive statistics.

But did you know quantiles are also valuable in regression, where they can answer a broader set of research questions than standard linear regression?

In standard linear regression, the focus is on estimating the mean of a response variable given a set of predictor variables.

In quantile regression, we can go beyond the mean of the response variable. Instead we can understand how predictor variables predict (1) the entire distribution of the response variable or (2) one or more relevant features (e.g., center, spread, shape) of this distribution.

For example, quantile regression can help us understand not only how age predicts the mean or median income, but also how age predicts the 75th or 25th percentile of the income distribution.

Or we can see how the inter-quartile range — the width between the 75th and 25th percentile — is affected by age. Perhaps the range becomes wider as age increases, signaling that an increase in age is associated with an increase in income variability.

In this webinar, we will help you become familiar with the power and versatility of quantile regression by discussing topics such as:

• Quantiles – a brief review of their computation, interpretation and uses;
• Distinction between conditional and unconditional quantiles;
• Formulation and estimation of conditional quantile regression models;
• Interpretation of results produced by conditional quantile regression models;
• Graphical displays for visualizing the results of conditional quantile regression models;
• Inference and prediction for conditional quantile regression models;
• Software options for fitting quantile regression models.

Join us on this webinar to understand how quantile regression can be used to expand the scope of research questions you can address with your data.

Note: This training is an exclusive benefit to members of the Statistically Speaking Membership Program and part of the Stat’s Amore Trainings Series. Each Stat’s Amore Training is approximately 90 minutes long.

Most analysts’ primary focus is to check the distributional assumptions with regards to residuals. They must be independent and identically distributed (i.i.d.) with a mean of zero and constant variance.

Residuals can also give us insight into the quality of our models.

In this webinar, we’ll review and compare what residuals are in linear regression, ANOVA, and generalized linear models. Jeff will cover:

• Which residuals — standardized, studentized, Pearson, deviance, etc. — we use and why
• How to determine if distributional assumptions have been met
• How to use graphs to discover issues like non-linearity, omitted variables, and heteroskedasticity

Knowing how to piece this information together will improve your statistical modeling skills.

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Mediators can affect the relationship between X and Y. Moderators can affect the scale and magnitude of that relationship. And sometimes the mediators and moderators affect each other.

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Linear regression with a continuous predictor is set up to measure the constant relationship between that predictor and a continuous outcome.

This relationship is measured in the expected change in the outcome for each one-unit change in the predictor.

One big assumption in this kind of model, though, is that this rate of change is the same for every value of the predictor. It’s an assumption we need to question, though, because it’s not a good approach for a lot of relationships.

Segmented regression allows you to generate different slopes and/or intercepts for different segments of values of the continuous predictor. This can provide you with a wealth of information that a non-segmented regression cannot.

In this webinar, we will cover (more…)