Document Sample

Linear Functions and Models Lesson 2.1 Problems with Data l Real data recorded l Experiment results l Periodic transactions l Problems l Data not always recorded accurately l Actual data may not exactly fit theoretical relationships l In any case … l Possible to use linear (and other) functions to analyze and model the data Fitting Functions Viscosity to Data Temperature 160 (lbs*sec/in2) 28 170 26 180 24 l Consider the data 190 21 200 16 given by this example 210 13 220 11 230 9 l Note the plot of the data points l Close to being in a straight line Finding a Line to Approximate the Data l Draw a line “by eye” l Note slope, y-intercept l Statistical process (least squares method) l Use a computer program such as Excel l Use your TI calculator Graphs of Linear Functions l For the moment, consider the first option Given the graph with tic marks = 1 l Determine l Slope l Y-intercept l A formula for the function l X-intercept (zero of the function) Graphs of Linear Functions l Slope – use difference quotient l Y-intercept – observe l Write in form l Zero (x-intercept) – what value of x gives a value of 0 for y? Modeling with Linear Functions l Linear functions will model data when l Physical phenomena and data changes at a constant rate l The constant rate is the slope of the function l Or the m in y = mx + b l The initial value for the data/phenomena is the y-intercept l Or the b in y = mx + b Modeling with Linear Functions l Ms Snarfblat's SS class is very popular. It started with 7 students and now, 18 months later has grown to 80 students. Assuming constant monthly growth rate, what is a modeling function? l Determine the slope of the function l Determine the y-intercept l Write in the form of y = mx + b Creating a Function from a Table l Determine slope by using x y 3 7 Answer: 4 8.5 5 10 6 11.5 Creating a Function from a Table l Now we know slope m = 3/2 l Use this and one of x y the points to determine 3 7 y-intercept, b 4 8.5 l Substitute an ordered 5 10 pair into 6 11.5 y = (3/2)x + b Creating a Function from a Table l Double check results l Substitute a different ordered pair into the formula l Should give a true statement x y 3 7 4 8.5 5 10 6 11.5 Piecewise Function l Function has different behavior for different portions of the domain Greatest Integer Function l = the greatest integer less than or equal to x l Examples l Calculator – use the floor( ) function Assignment l Lesson 2.1A l Page 88 l Exercises 1 – 65 EOO Finding a Line to Approximate the Data l Draw a line “by eye” l Note slope, y-intercept l Statistical process (least squares method) l Use a computer program such as Excel l Use your TI calculator 15 You Try It Weight Calories 100 2.7 l Consider table of ordered pairs 120 3.2 showing calories per minute 150 4.0 170 4.6 as a function of body weight 200 5.4 l Enter data into data matrix of 220 5.9 calculator l APPS, Date/Matrix Editor, New, 16 Using Regression On Calculator l Choose F5 for Calculations l Choose calculation type (LinReg for this) l Specify columns where x and y values will come from 17 Using Regression On Calculator l It is possible to store the Regression EQuation to one of the Y= functions 18 Using Regression On Calculator l When all options are set, press ENTER and the calculator comes up with an equation approximates your data Note both the original x-y values and the function which approximates the data 19 Using the Function l Resulting function: l Use function to find Calories Weight Calories 100 2.7 for 195 lbs. 120 3.2 l C(195) = 5.24 150 4.0 170 4.6 This is called extrapolation 200 5.4 220 5.9 l Note: It is dangerous to extrapolate beyond the existing data l Consider C(1500) or C(-100) in the context of the problem l The function gives a value but it is not valid 20 Interpolation l Use given data Weight Calories l Determine 100 2.7 proportional 120 3.2 “distances” 150 4.0 170 4.6 25 x 30 195 ?? 0.8 200 5.4 220 5.9 Note : This answer is different from the extrapolation results 21 Interpolation vs. Extrapolation l Which is right? l Interpolation l Between values with ratios l Extrapolation l Uses modeling functions l Remember do NOT go beyond limits of known data 22 Correlation Coefficient l A statistical measure of how well a modeling function fits the data l -1 ≤ corr ≤ +1 l |corr| close to 1 ó high correlation l |corr| close to 0 ó low correlation l Note: high correlation does NOT imply cause and effect relationship 23 Assignment l Lesson 2.1B l Page 94 l Exercises 85 – 93 odd

DOCUMENT INFO

Shared By:

Categories:

Tags:

Stats:

views: | 1 |

posted: | 6/9/2014 |

language: | English |

pages: | 24 |

OTHER DOCS BY pptfiles

How are you planning on using Docstoc?
BUSINESS
PERSONAL

By registering with docstoc.com you agree to our
privacy policy and
terms of service, and to receive content and offer notifications.

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.