STAT 2103 Lecture 22: Multiple Regression
9 May 2018
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STAT 2103 – Lecture 22 – Multiple Regression
Multiple Regression: Predicting One Variable from Several Others
• Predicting a single Y variable from two or more X variables
– Describe and Understand the Relationship
• Understand the effect of one X variable while holding the others fixed
– Forecast (Predict) a New Observation
• Lets you use all available information (X variables) to find out about what you
don’t know (the Y variable for this new situation)
– Adjust and Control a Process
• because the regression equation (you hope) tells you what would happen if
you made a change
Example: Magazine Ads
• Input Data
– To predict cost of ads from magazine characteristics
Intercept a:
• Predicted Page Costs
= a + b1 X1 + b2 X2 + b3 X3
= –22,385 + 10.50658(Audience) – 20,779(Percent Male)
+ 1.09198(Median Income)
• Intercept a = –22,385
• Essentially a base rate, representing the dollar cost of advertising in a magazine
that has no audience, no male readers, and zero income level
• But there are no such magazines
• intercept a is merely there to help achieve best predictions
Document Summary
Stat 2103 lecture 22 multiple regression. Multiple regression: predicting one variable from several others: predicting a single y variable from two or more x variables. Describe and understand the relationship: understand the effect of one x variable while holding the others fixed. Lets you use all available information (x variables) to find out about what you don"t know (the y variable for this new situation) Adjust and control a process: because the regression equation (you hope) tells you what would happen if you made a change. To predict cost of ads from magazine characteristics. Income: on average, page costs are estimated to be . 51 higher for a magazine with one more (thousand) audience, as compared to another magazine with the same percent male and median income. We will see that percent male is not significant. = a + b1 x1 + b2 x2 + b3 x3.
