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Regression Analysis

Regression Analysis. Modeling Relationships. Dependent Variable. Independent Variables. Regression Analysis. Regression Analysis is a study of the relationship between a set of independent variables and the dependent variable.

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Regression Analysis

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  1. Regression Analysis Modeling Relationships

  2. Dependent Variable Independent Variables Regression Analysis Regression Analysis is a study of the relationship between a set of independent variables and the dependent variable. The Linear Equation representing the ‘true’ or population relationship:

  3. Variables Dependent Variable: Also called the predicted variable. Its value depends on, or can be predicted by the independent variables. Independent Variables: Also called the predictor variables. These can be measured directly, and are used to predict the dependent (or to simply understand it better).

  4. Modeling Process

  5. The Data A portion of the data is shown below. See Spreadsheet for all data.

  6. Preliminary Analyses The table below shows some descriptive statistics for each variable. What basic statements about our data can we make from this?

  7. Capacity by Gender, Smoking Does there appear to be a relationship between, Smoking, Gender, and Lung Capacity?

  8. Distributions

  9. Bivariate Analysis – Matrix Plot

  10. Capacity distribution by Gender, Smoking Men have a larger lung capacity than women, on average. Non-Smokers have a larger lung capacity than smokers on average. What about the variance?

  11. Simple Regression How well can exercise time alone predict the lung capacity?

  12. Multiple Regression How do all the Xs together help predict y?

  13. Final Model 1656.937 + 202.104 * Gender + 50.359 * Height – 279.025 * Smoker + 11.259 * Exercise

  14. Prediction Exercise • Predict the lung capacity for a non-smoking female who does not exercise, and is 66 inches tall, based on the model above. • What would be the predicted value if she smoked? • What would it be for a male in both the above cases?

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