LSP 120 Week 1

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

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

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

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

Linear modeling Week 1

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

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

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

Linear Equations Multi-step problem: 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. 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 Write an equation to model the school’s enrollment since y=30x+1400 y=30x+1400 What is the enrollment in 1999? What is the enrollment in 1999? y=30(3)+1400=1490 y=30(3)+1400=1490

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

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

Linear Modeling Steps 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.

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

Example – by hand Step 1: Plot the points Step 1: Plot the points

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

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

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

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

Example – using Excel Open up BreastCancer xls Open up BreastCancer xlsBreastCancer xls (under excel files tab on qrc website) (under excel files tab on qrc website)

Example – using Excel

y = x y = x You can use the equation to predict the future or look to the past. You can use the equation to predict the future or look to the past. R² = R² = The R-squared value tells you how reliable your equation is. The closer the value is to 1, the better it is. The R-squared value tells you how reliable your equation is. The closer the value is to 1, the better it is.

Example – using Excel y = x y = x What would be the rate of breast cancer in 2008? What would be the rate of breast cancer in 2008? y = (2008) = y = (2008) =

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

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

Example – using Excel

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

In class activity: In class activity: Activity 1 Activity 1 Homework: Homework: Homework 1 Homework 1