DOC PREVIEW
UT Knoxville STAT 201 - Chapter 07 Student 0117

This preview shows page 1-2-3-23-24-25-26-47-48-49 out of 49 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 49 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 49 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 49 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 49 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 49 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 49 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 49 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 49 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 49 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 49 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 49 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

Slide 1Slide 2Fat Versus Protein: An ExampleThings to Look For in ScatterplotsCorrelation ConditionsThe Linear ModelThe Linear Model (Cont.)ResidualsIllustration of a ResidualResiduals (cont.)How Well Does Any Line Fit the Data?How Well Does Any Line Fit the Data?In Class Activity - RegressionIn Class Activity – Regression (Cont.)In Class Activity – Regression (Cont.)The Linear Model - RevisitedInterpreting the Coefficients - ExampleInterpreting the Coefficients - ExampleIn-Class Activity - Meaningless Intercepts?In-Class Activity - Meaningless Intercepts? (Cont.)Slide 21The Least Squares LineThe Least Squares Line (cont.)Fat Versus Protein: An ExampleConditions for RegressionRoles for VariablesIn-Class Activity - Roles for VariablesInterest Rates vs. Mortgages - ExampleInterest Rates vs. Mortgages (Cont.)Interest Rates vs. Mortgages (Cont.)Interest Rates vs. Mortgages (Cont.)Slide 32Interest Rates vs. Mortgages (Cont.)Interest Rates vs. Mortgages (Cont.)Slide 35Residuals RevisitedResiduals Revisited (cont.)Residuals Revisited (cont.)Residuals for Interest Rates vs. Mortgages DataSlide 40R2—The Variation Accounted ForR2—The Variation Accounted For (cont.)R2—The Variation Accounted For (cont.)R2—The Variation Accounted For (cont.)Interest Rates vs. Mortgages - RevisitedHow Big Should R2 Be?Using the Regression Equation to Make Predictions - PrecautionsSlide 48Regression Conditions - Review1Chapter07 Presentation 0117Copyright © 2014, 2012, 2009 Pearson Education, Inc.Chapter 7Linear Regression2Chapter07 Presentation 0117Copyright © 2014, 2012, 2009 Pearson Education, Inc.7.1 and 7.2Least Squares: The Line of “Best Fit”The Linear ModelChapter07 Presentation 01173Copyright © 2014, 2012, 2009 Pearson Education, Inc.Fat Versus Protein: An ExampleThe following is a scatterplot of total fat versus protein for 122 items on the Burger King menu:Chapter07 Presentation 01174Copyright © 2014, 2012, 2009 Pearson Education, Inc.Things to Look For in ScatterplotsDirectionFormStrengthUnusual featuresChapter07 Presentation 01175Copyright © 2014, 2012, 2009 Pearson Education, Inc.Correlation ConditionsBefore you use correlation, you must check several conditions:Quantitative Variables ConditionStraight Enough ConditionNo Outliers ConditionChapter07 Presentation 01176Copyright © 2014, 2012, 2009 Pearson Education, Inc.The Linear ModelRemember from Algebra that a straight line can be written as: In Statistics we use a slightly different notation:y mx b= +0 1ˆy b b x= +Chapter07 Presentation 01177Copyright © 2014, 2012, 2009 Pearson Education, Inc.The Linear Model (Cont.)The linear model that “best fits” our Burger King data is:How well does this model fit our data?Chapter07 Presentation 01178Copyright © 2014, 2012, 2009 Pearson Education, Inc.ResidualsThe difference between the observed value (y) and its associated predicted value ( ) is called the residual.If the model fits the data well, these will all be close to zero.ˆresidual observed predicted y y= - = -yˆChapter07 Presentation 01179Copyright © 2014, 2012, 2009 Pearson Education, Inc.Illustration of a ResidualChapter07 Presentation 011710Copyright © 2014, 2012, 2009 Pearson Education, Inc.Residuals (cont.)The BK Tendercrisp chicken sandwich (no mayo) has x=31 grams of protein.The model says it should have y=36.6 grams of fat.In fact, it has y=22 grams of fat.Calculate the residual for this observation and interpret it. ÙChapter07 Presentation 011711Copyright © 2014, 2012, 2009 Pearson Education, Inc.How Well Does Any Line Fit the Data?Let’s calculate ALL the residuals.Can we add them up, and claim if the sum is small, the line fits well?Chapter07 Presentation 011712Copyright © 2014, 2012, 2009 Pearson Education, Inc.How Well Does Any Line Fit the Data?How did we solve this dilemma when calculating a measure of distance from y-bar (i.e., when calculating the standard deviation)?So, how can we define the “best fitting” line?Chapter07 Presentation 011713Copyright © 2014, 2012, 2009 Pearson Education, Inc.In Class Activity - RegressionUsing the tape measure provided, wrap the tape measure around your head (around the middle of your forehead, and level all the way around your head). Have your partner read the measurement (in cm, to nearest tenth) and write it in the table on a following page. Have your partner do the same.Then, hold the “zero cm” measurement of the tape measure at the edge of your shoulder and run it down your arm to the tip of your longest finger. Have your partner read this measurement (in cm, to nearest tenth) and write it in the table. Have your partner do the same. Example: 61.5 cm (or maybe 61.6 cm)Chapter07 Presentation 011714Copyright © 2014, 2012, 2009 Pearson Education, Inc.Now, take turns using the tape measure to determine the circumference of your own wrists (in cm, to nearest tenth). Wrap the tape snugly but not tight around your wrist as indicated in the image below. Again, be sure to use the “zero cm” on the tape to make your measurement, not the end of the tape.In Class Activity – Regression (Cont.)Chapter07 Presentation 011715Copyright © 2014, 2012, 2009 Pearson Education, Inc.In Class Activity – Regression (Cont.)Write these data (all 7 columns) on a sheet of notebook paper and turn it in to your instructor (one sheet per team).Your instructor will collect the data, put it into a JMP file (excluding your initials) and email the class’s results to you for the next class. Please, if you have one, BRING YOUR LAPTOP TO THE NEXT CLASS. Your InitialsYour GenderYour Head CircumferenceYour Arm LengthYour Left Wrist CircumferenceYour Right Wrist CircumferenceNotesChapter07 Presentation 011716Copyright © 2014, 2012, 2009 Pearson Education, Inc.The Linear Model - Revisited The coefficient b1 is the slope, which tells us how rapidly changes with respect to x.The coefficient b0 is the intercept, which tells where the line hits (intercepts) the y-axis.ˆyRecall our linear model is:0 1ˆy b b x= +Chapter07 Presentation 011717Copyright © 2014, 2012, 2009 Pearson Education, Inc.Interpreting the Coefficients - ExampleFor our Burger King data, our model is:The slope is b1 = 0.91 grams of fat per gram of protein. For every additional gram of protein, we would expect there to be an additional 0.91 grams of fat, on average.Chapter07 Presentation


View Full Document

UT Knoxville STAT 201 - Chapter 07 Student 0117

Documents in this Course
Chapter 8

Chapter 8

43 pages

Chapter 7

Chapter 7

30 pages

Chapter 6

Chapter 6

43 pages

Chapter 5

Chapter 5

23 pages

Chapter 3

Chapter 3

34 pages

Chapter 2

Chapter 2

18 pages

Chapter 1

Chapter 1

11 pages

Load more
Download Chapter 07 Student 0117
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Chapter 07 Student 0117 and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Chapter 07 Student 0117 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?