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LSP 120

LSP 120. Week 1. True or False?. Chickens can live without a head. True The Great Wall of China is the only manmade structure visible from space. False. It takes seven years to digest gum. False. True or false?. Yawning is “contagious” True

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LSP 120

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  1. LSP 120 Week 1

  2. True or False? • Chickens can live without a head. • True • The Great Wall of China is the only manmade structure visible from space. • False. • It takes seven years to digest gum. • False

  3. True or false? • Yawning is “contagious” • True • Water drains backwards in the Southern Hemisphere due to the Earth’s rotation. • False

  4. True or false? • Eating a poppy seed bagel mimics opium use. • True • A penny dropped from the top of a tall building could kill a pedestrian. • False. • Shaving hair causes it to grow back faster, darker, or coarser. • False

  5. True or False • Reading in dim light ruins your eyesight. • False • Eating turkey makes people especially drowsy. • False • Hair and fingernails continue to grow after death. • False

  6. Linear modeling Week 1

  7. Linear Equations • Model: y=mx+b • Graph: a line

  8. Linear Equations • y=mx+b • b stands for y-intercept • Starting point • x = 0 • m is the slope (the rate of change).

  9. Linear Equations • Write the equation for the following scenario using y=mx+b. • A car rental company charges a flat fee of $40 and an additional $.20 per mile to rent a car. • y=.2x+40 • What if the flat fee is $50 and the additional cost per mile is $.30? • y=.3x+50

  10. Linear Equations • Multi-step problem: • In 1996, the enrollment in a high school was approximately 1400 students. During the next three years, the enrollment increased by approximately 30 students per year. • Write an equation to model the school’s enrollment since 1996. • y=30x+1400 • What is the enrollment in 1999? • y=30(3)+1400=1490

  11. Linear Equations • If the trend continues, when will the enrollment reach 2000? • 2000 = 30x + 1400 • 600 = 30x • x = 20 years, in 2016

  12. Linear modeling • When can we use it? • When our data is best described by a line. • What’s the point? • To get a linear equation (y=mx+b) that best describes our data. • Then we can use the equation to predict the future or look back into the past.

  13. Linear Modeling • Steps 1. Plot data points 2. Draw a best fit line (AKA trendline, regression line). 3. Find the equation of the line 4. Use the equation of the line to look ahead or look back.

  14. Example – by hand • The Table lists the number of households, in millions, in the US that owned computers between 1984 and 1991. Approximate the best-fitting line for this data.

  15. Example – by hand • Step 1: Plot the points

  16. Example – by hand • Step 2: Draw the trendline (best fit line, regression line)

  17. Example – by hand • Step 3: Find the equation of the line • Pick two points that are on the line • (1987,16) (1989,21.5) • Find the slope • Slope=(21.5-16)/(1989-1987)=5.5/2=2.75 • Find the equation of the line • y-16=2.75(x-1987) • y=2.75x-5448.25

  18. Example – by hand • Step 4: Use the equation (y=2.75x-5448.25) to predict the future: How many households would own computers in 2003? • y=2.75 (2003)-5448.25 = 60 million • How does our prediction fare? • Actual number of households: 68 million

  19. Linear Modeling • Steps • Plot data points • Draw a best fit line (AKA trendline, regression line). • Find the equation of the line • Use the equation of the line to look ahead or look back.

  20. Example – using Excel • Open up BreastCancer1990-2003.xls • (under excel files tab on qrc website)

  21. Example – using Excel

  22. Example – using Excel

  23. Example – using Excel

  24. Example – using Excel

  25. Example – using Excel

  26. Example – using Excel

  27. Example – using Excel • y = -0.378x + 786.5 • You can use the equation to predict the future or look to the past. • R² = 0.711 • The R-squared value tells you how reliable your equation is. The closer the value is to 1, the better it is.

  28. Example – using Excel • y = -0.378x + 786.5 • What would be the rate of breast cancer in 2008? • y = -.378 (2008) + 786.5 = 27.476

  29. Predicting • How many years is too many when predicting the future? • Depends on the R squared value and • The amount of data we have

  30. Example – using Excel • You can graphically show the prediction • Right click on equation • Choose “Format Trendline” • Under forecast, type in 5 (because 2008 is 5 years after 2003)

  31. Example – using Excel

  32. Example – using Excel

  33. Summary • Concept: Linear modeling • y=mx+b • Trendline, regression line, best fit line • Excel Tools: • Insert: scatter plot • Add trendline • Forecast

  34. In class activity: • Activity 1 • Homework: • Homework 1

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