1 / 15

SECTION 2.2

SECTION 2.2. BUILDING LINEAR FUNCTIONS FROM DATA. LINEAR CURVE FITTING. STEP 1 : Ask whether the variables are related to each other. STEP 2 : Obtain data and verify a relation exists. Plot the points to obtain a scatter diagram . STEP 3 : Find an equation which describes this relation.

oshin
Download Presentation

SECTION 2.2

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. SECTION 2.2 • BUILDING LINEAR FUNCTIONS FROM DATA

  2. LINEAR CURVE FITTING • STEP 1: Ask whether the variables are related to each other. • STEP 2: Obtain data and verify a relation exists. Plot the points to obtain a scatter diagram. • STEP 3: Find an equation which describes this relation.

  3. FINDING AN EQUATION FOR LINEARLY RELATED DATA • A farmer collected the following data, which shows crop yields for various amounts of fertilizer used.

  4. Fertilizer (X lbs) Yield (Y bushels) 0 4 0 6 5 10 5 7 10 12 10 10 15 15 15 17 20 18 20 21 25 23 25 22

  5. GETTING A SCATTER PLOT OF THE DATA Ensure that all equations in the Y= menu are cleared out or disabled. Input the data into the lists in the statistics editor: STAT 1:Edit Turn on a Statistics Plotter and set the desired parameters: 2nd Y= Push Zoom and choose ZoomStat.

  6. GETTING A LINE OF BEST FIT Verify by the scatter plot that the data has a linear relationship. Go to the home screen, press STAT, arrow to CALC, and choose LinReg. A linear regression equation will appear in the home screen.

  7. GRAPHING THE REGRESSION EQUATION To put the regression equation in the Y= menu: 1. Push Y= 2. Push VARS, choose Statistics, arrow to EQ, and choose RegEQ. Now push GRAPH.

  8. MAKING A PREDICTION Use the Linear Regression Equation to Estimate the Yield if the farmer uses 17 pounds of fertilizer. 1. Go to home screen 2. Go into YVARS, choose Function, Choose Y1. 3. Type in (17).

  9. MAKING A PREDICTION Our prediction is that the crop yield for 17 Pounds of fertilizer per 100 ft2 will be 17 Bushels

  10. CONCLUSION OF SECTION 2.2

  11. VARIATION Relationships between variables are often described in terms of proportionality. For Example: Force is proportional to acceleration. Pressure and volume of an ideal gas are inversely proportional.

  12. DIRECT VARIATION Let x and y denote two quantities. Then y varies directly with x, or y is directly proportional to x, if there is a nonzero number k such that y = kx constant of proportionality

  13. EXAMPLE For a certain gas enclosed in a container of fixed volume, the pressure P (in newtons per square meter) varies directly with temperature T (in kelvins). If the pressure is found to be 20 newtons/m2 at a temperature of 60 K, find a formula that relates pressure P to temperature T. Then find the pressure P when T = 120 K.

  14. SOLUTION First, we know that P varies directly with T. P = k T And, we know P = 20 when T = 60. Thus, 20 = k(60)

  15. SOLUTION The formula, then, is Now, we must find P when T = 120K P = 40 newtons per square meter

More Related