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

Water drains backwards in the Southern Hemisphere due to the Earth’s rotation. False

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

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

Linear modeling

Week 1

Linear Equations

Model: y=mx+b Graph: a line

Linear Equations

y=mx+b b stands for y-intercept

Starting point x = 0

m is the slope (the rate of change).

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

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

Linear Equations

If the trend continues, when will the enrollment reach 2000?

2000 = 30x + 1400 600 = 30x x = 20 years, in 2016

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.

Linear Modeling

Steps1. Plot data points2. Draw a best fit line (AKA trendline,

regression line).3. Find the equation of the line4. 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 1991. Approximate the best-fitting line for this data.

Year 1984 1985

1986

1987

1988

1989

1990

1991

Households 6.0 11.3 14.2 16.2 19.2 21.3 25.3 26.6

Example – by hand

Step 1: Plot the points

0

5

10

15

20

25

30

1983 1984 1985 1986 1987 1988 1989 1990 1991 1992

Example – by hand

Step 2: Draw the trendline (best fit line, regression line)

0

5

10

15

20

25

30

1983 1984 1985 1986 1987 1988 1989 1990 1991 1992

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

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

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.

Example – using Excel

Open up BreastCancer1990-2003.xls (under excel files tab on qrc website)

Example – using Excel

Example – using Excel

Example – using Excel

Example – using Excel

Example – using Excel

Example – using Excel

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.

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

Predicting

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

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)

Example – using Excel

Example – using Excel

Summary

Concept: Linear modeling y=mx+b Trendline, regression line, best fit line

Excel Tools: Insert: scatter plot Add trendline Forecast

In class activity: Activity 1

Homework: Homework 1