Regression Notes

Regression Notes - Simple Linear Regression Modeling the...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Sections 6.1 and 6.2 Page 1 Simple Linear Regression Modeling the Relationship Between Two Quantitative Variables h If we can model the relationship between two quantitative variables, we can use one variable, X, to predict another variable, Y. o Use height to predict weight. o Use percentage of hardwood in pulp to predict the tensile strength of paper. o Use square feet of warehouse space to predict monthly rental cost. h We use data to create the model o Observational Study o Height and Weight o Square footage of warehouse space and cost. h Designed experiment o Percentage of hardwood and tensile strength. o Time it takes for primer to dry with different chemical contents. Simple Linear Regression o Simple: only one predictor variable o Linear: Straight line relationship o Regression: Fit data to (straight line) model Predictor/Independent Variable Response/Dependent Variable
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Sections 6.1 and 6.2 Page 2 Use Scatter Plot to See Relationship h Linear h Curve h Clustered h No relationship Example. The rate at which a spilled volatile liquid will spread across a surface was study by a group of chemical engineers. The mass (in pounds) of a 50-gallon methanol spill after a period ranging form 0 to 60 milliseconds was calculated. What is the relationship between time and mass? 60 50 40 30 20 10 0 7 6 5 4 3 2 1 0 TIME MASS Example. In a chemical process, batches of liquid are passed through a bed containing an ingredient that is absorbed by the liquid. We will attempt to relate the absorbed percentage of the ingredient (y) to the amount of liquid in the batch (x). The fitted Deterministic Model gG±²G³´ µ¶·¸±¶G¹ º »2263.44 ¼ 501 ½ µ¾¸¿³´ 4.5 5.0 5.5 6.0 6.5 0 200 400 600 800 1000 1200 amt percent 4.5 5.0 5.5 6.0 6.5 amt
Background image of page 2
Sections 6.1 and 6.2 Page 3 The Probabilistic Model h Model accounts for the variation around the line o y = deterministic model + random error o gG±²G³´ µ¶·¸±¶G¹ º »2263.44 ¼ 501 ½ µ¾¸¿³´ ¼ ±À³¹¸¾ G±±¸± Regression Equation Á º  à ¼ Â Ä Å ¼ Æ Ç º ÈÉÁÊ The regression line is the estimate of the mean value of y at a given x. Estimating β
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 13

Regression Notes - Simple Linear Regression Modeling the...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online