LeastSquares Regression Linear Regression 3 2 Part 2

  • Slides: 20
Download presentation
Least-Squares Regression: Linear Regression 3. 2 Part 2 of 2 Reference Text: The Practice

Least-Squares Regression: Linear Regression 3. 2 Part 2 of 2 Reference Text: The Practice of Statistics, Fourth Edition. Starnes, Yates, Moore

Warm Up A) B) C) D) E) Write a few sentences describing the graph

Warm Up A) B) C) D) E) Write a few sentences describing the graph in context. Calculate the LSRL and report your answer in context. Describe the slope in context. Describe the y-intercept in context. Predict a backpack weight based on a body weight of 115 pounds, interpret your results in context. F) Predict a backpack weight based on a body weight of 220 pounds. G) Why is the value you found in (F) not a reasonable prediction? H) Find and interpret the residual of someone who weights 115 lbs when her backpack weight was 17 lbs.

Today’s Objectives •

Today’s Objectives •

Formulas for Slope and y-intercept •

Formulas for Slope and y-intercept •

Example •

Example •

Example •

Example •

Example •

Example •

Non Exercise Activity of Fat Gain •

Non Exercise Activity of Fat Gain •

Check for understanding •

Check for understanding •

Survey Says… C 60. 6% of the variation in fat gain is accounted for

Survey Says… C 60. 6% of the variation in fat gain is accounted for by the least-squares line

SSE and SST What do they mean? •

SSE and SST What do they mean? •

WARNING! •

WARNING! •

• Interpreting Computer Regression Output Least-Squares Regression A number of statistical software packages

• Interpreting Computer Regression Output Least-Squares Regression A number of statistical software packages produce similar regression output. Be sure you can locate • the slope b, • the y intercept a, • and the values of s and r 2.

Outliers! Influencing my LSRL? Definition: An outlier is an observation that lies outside the

Outliers! Influencing my LSRL? Definition: An outlier is an observation that lies outside the overall pattern of the other observations. Points that are outliers in the y direction but not the x direction of a scatterplot have large residuals. Other outliers may not have large residuals. An observation is influential for a statistical calculation if removing it would markedly change the result of the calculation. Points that are outliers in the x direction of a scatterplot are often influential for the leastsquares regression line. • Lets look at an illustration!

Outlier, no Outlier Look at the r value!

Outlier, no Outlier Look at the r value!

Determining of its influential? • The best way to verify that a point is

Determining of its influential? • The best way to verify that a point is influential is to find the regression line both with and without the unusual point. If the line moves more than a small amount when the point is deleted, the point is influential. – There is no rule for determining outliers in scatterplots • Remember: We are only investigation the influential behavior of these points, in practice it would be wrong to delete inconvenient observations without a good justification!

Video about Linear Regression

Video about Linear Regression

Today’s Objectives •

Today’s Objectives •

Homework Continue working on Chapter 3 Reading Guide 3. 2 Part 2 HW Worksheet

Homework Continue working on Chapter 3 Reading Guide 3. 2 Part 2 HW Worksheet

4 3 LeastSquares Regression 1 Regression Lines LeastSquares4 3 LeastSquares Regression 1 Regression Lines LeastSquares
Ordinary LeastSquares Outline Linear regression Geometry of leastsquaresOrdinary LeastSquares Outline Linear regression Geometry of leastsquares
Regression Linear regression Simple linear regression 1 MultipleRegression Linear regression Simple linear regression 1 Multiple
Regression Analysis Simple Linear Regression Multiple Linear RegressionRegression Analysis Simple Linear Regression Multiple Linear Regression
Regression Methods Linear Regression Simple linear regression oneRegression Methods Linear Regression Simple linear regression one
Regression Methods Linear Regression Simple linear regression oneRegression Methods Linear Regression Simple linear regression one
Regression Methods Linear Regression Simple linear regression oneRegression Methods Linear Regression Simple linear regression one
Linear Regression Outline Linear Regression Analysis Linear trendLinear Regression Outline Linear Regression Analysis Linear trend
Nonlinear LeastSquares Regularized LeastSquares Why nonlinear The modelNonlinear LeastSquares Regularized LeastSquares Why nonlinear The model
LeastSquares regression line A regression line is aLeastSquares regression line A regression line is a
LEASTSQUARES REGRESSION 3 2 Least Squares Regression LineLEASTSQUARES REGRESSION 3 2 Least Squares Regression Line
Regression Line Definition The leastsquares regression line ofRegression Line Definition The leastsquares regression line of
Objectives 2 3 Leastsquares regression p Regression linesObjectives 2 3 Leastsquares regression p Regression lines
LEASTSQUARES REGRESSION 3 2 Interpreting Computer Regression OutputLEASTSQUARES REGRESSION 3 2 Interpreting Computer Regression Output
Regression Line Definition The leastsquares regression line ofRegression Line Definition The leastsquares regression line of
LeastSquares Regression Regression Line Model n It hasLeastSquares Regression Regression Line Model n It has
LEASTSQUARES REGRESSION Section 3 3 Regression line ALEASTSQUARES REGRESSION Section 3 3 Regression line A
Linear Regression The Science of Predicting Outcome LeastSquaresLinear Regression The Science of Predicting Outcome LeastSquares
General Linear LeastSquares and Nonlinear Regression Berlin ChenGeneral Linear LeastSquares and Nonlinear Regression Berlin Chen