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week6_lec1-2_regression_s09hdd-1

# week6_lec1-2_regression_s09hdd-1 - Get Fired-Up l Start l...

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Get Fired-Up!! l Start one computer per pair l Get on Blackboard l Go to: Lecture Slides, Prof. Diefes-Dux Folder l Save: regression_examples_diefes-dux.xlsx to desktop or H: drive l Start Excel – open saved file l Start MATLAB

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Due Today l MEA 1 Peer Critique (Due Today 2/17) Reminder: It is critical that you complete all parts of the MEA 1 sequence. Failure to complete any part will lock you out of the rest of the sequence and could result in a grade of zero on MEA 1. l Regression with Linear Scales l Notes pp. 78-84 l Textbook Ch 12 pp. 444-446; 448-449
Checking for Understanding… ? 5 1 = = i i (not in notes)

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Plotting and Regression with Linear Scales Learning Objectives (Notes: 78-84) At the end of this class period, you will begin to be able to: l State why we do regression l Produce the equation of a regression line l Manually l Using MATLAB l Using Excel l Define, calculate, and explain the use of l SSE sum of the squares of errors l SST sum of the squares of deviations l r2 coefficient of determination
A regression is a method of creating a model of a system l Paired data sets l We’ve measured both X and Y l We think that Y may depend on X l So first we plot the data X Y The line is potentially a MODEL of the data. Is it a GOOD model?

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When using regression, we assume that one variable is a function of another l Cause-and-Effect l Distance is a function of launch angle l Reaction rate is a function of temperature l Changes over Time (temporal changes) l Coffee (in cup) temperature is function of time l Gross Domestic Product (GDP) is a function of time l Spatial Profile l The number of pedestrians crossing the street is a function of location along the street
You probably learned in mathematics that functions can be represented four ways l Verbally : describe the relationship l Numerically : tabulate the data l Visually : show us a graph l Symbolically : use an equation as a model Today, we’ll focus on the last two: l Visually: Fit a “best” regression line to graphed data l Symbolically: Find the “best” regression line equation

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What is a linear regression analysis? Given a set of data, develop a line y = a x + b where: l (x,y) represents the raw data points l a is the slope (change in y over change in x ) l b is the y -intercept when x = 0 that “best fits” data How do we determine a and b? How do we determine what is the “best” fit?
Telephone Expenditures (1981-1999) y = a x + b where: l (x,y) represents the raw data points of year l x for annum l y for phone expenditures l a is the slope of the line in phone cost/year l b is the intercept, which doesn't mean much here, since it's the phone cost in 0 A.D. Best Fit Line Raw Data Notes p. 79

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Two-Point Method to Determine Slope and Intercept Point 1 (1981,360) and Point 2 (1999,849) b = C – m A = 360 – 27.17(1981) = -53464 Our equation for the line through the first and last points is: y = 27.17 x - 53464 2 1 2 1 849 360 27.17 1999 1981 y y m x x - - = = = - -
Two-Point Method to Determine Slope and Intercept Alternatively, compute b using both points Solve simultaneously for b Our equation for the line through the first and last points is

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week6_lec1-2_regression_s09hdd-1 - Get Fired-Up l Start l...

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