4-5 Scatter Plots and Lines of Fit When data is taken from real-world situations, it very often does not fall in an exact line; however, it does often display a linear trend, and that trend can have a positive, negative, or no correlation. This means that it generally displays a positive ʻslopeʼ, negative ʻslopeʼ, or does not fall in any linear pattern at all. The graphics I used above use the word ʻrelationshipʼ, but we will use the term ʻcorrelationʼ. Ex. 1CYP (see pg. 245) When we graph data and make a scatter plot, and observe a positive or negative correlation, we can use a linear function to model the data. To do this: *Draw a line through two of the points that seems to best fit the data. (line of fit) *Use the two points to write the equation of the line. *Use the equation to make predictions of data of the same kind. (interpolation/extrapolation) (interpolation - predict values within the range of data, extrapolation - predict values outside the range of data, ie, future) Ex. 2B FARMING The table shows the percent of U.S. workers in farm occupations. Farm Workers Years since 1900 Percent of U.S. Workers 0 20 40 60 80 94 37.5 27 17.4 6.1 2.7 2.5 Source: The World Almanac *Draw a scatter plot, determine a correlation, if any, and write a line of fit. Ex. 3B Now estimate the percent of U.S. workers in farm occupations in 1996. (4-2) Biblical Integration Knowing vs. Predicting While it is good to 'know the state of your flocks', acting upon predicted outcomes that are based upon a worldly trend is not complete wisdom. God has given us a way to know our future, rather than predict it based on the past. God's voice is always reliable. "It had been revealed to him by the Holy Spirit that he would not die before he had seen the Lord's Christ." Luke 2:26 "As for you, the anointing you received from him remains in you, and you do not need anyone to teach you. But as his anointing teaches you about all things and as that anointing is real, not counterfeit, just as it has taught you, remain in him." I John 2:27 "By faith Noah, when warned about things not yet seen, in holy fear built an ark to save his family. By his faith he condemned the world and became heir of the righteousness that comes by faith." Hebrews 11:7 "He makes my feet like those of a deer and gives me sure footing on high places." Psalm 18:33 Problems for Practice: 5, 7, 9, 11, 15, 19 Complete on notebook paper or the back of these printed notes, in notes section of binder. Check with the back of the book. Place a colored check by correct answers. Correct incorrect answers to the right. Use Hotmath if you need help. USE YOUR NOTES AS YOU WORK THESE!!! Also complete/check the following Spiral/Skills Review: 21, 31 *Don’t forget that extra examples and even a personal tutor explaining examples can be found on your textbook website. Links found on syllabus. (4-2)