Project 1: Linear Regression

Get instructions for creating trendlines:

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Part 1

Graph the following points, representing the typical atmospheric pressure in a variety of places (in millibars) and their associated boiling points of water (in degrees Celsius).


place
Boone, NC
Dead Sea, Asia
Denali Peak, AK
Gallup, NM
Landsdale, PA
Leadville, CO
Mauna Kea, HI
pressure
(mb)		boiling
point (C)
900 96.7
1100102.3
500 81.3
800 93.5
100099.6
700 90.0
600 86.0
 Before adding the trendline to the graph (using the instructions above), try to predict the following:
  • Whether the slope is positive or negative.
  • The approximate value of the slope.
  • The approximate value of the y-intercept.
Then enter the actual values below, as well as the equation of the trendline.
How close were your predicted values?     Now, use this equation to predict the boiling point of water in Denver, CO (pressure of 834 mb):
Do you think this predicted value will be close to the real value? yes no
Part 2

Graph the following points, representing the population of various states in the United States (in millions of people) and the number of Tim Hortons café locations in those states.


state
Michigan
New Jersey
New York
North Carolina
Ohio
Pennsylvania
Texas
population
(millions)		café
locations
10.04 190
9.295
19.57 269
10.84 0
11.79119
12.96 18
30.50 2
 Before adding the trendline to the graph (using the instructions above), try to predict the following:
  • Whether the slope is positive or negative.
  • The approximate value of the slope.
  • The approximate value of the y-intercept.
Then enter the actual values below, as well as the equation of the trendline.
How close were your predicted values?     Now, use this equation to predict the number of Tim Hortons cafés in Virginia (population 8.72 million):
Do you think this predicted value will be close to the real value? yes no
Part 3
Generate your own data points using a six-sided die (or try random.org) by doing the following:
  • Roll a six-sided die many times, and record on which rolls you get a six.
    • Do not restart your counting after rolling a six, just continue counting from where you left off.
  • Continue this until you have rolled ten sixes.
    • If it takes more than 100 rolls, check the die you are using.)
  • Fill in the data points on the chart to the right. The x coordinates for the points will be the numbers from 1 to 10, while the y coordinates will be the rolls on which you rolled a six.
    • For example: if in the first 25 rolls, you rolled a six on the 7th, 10th, 15th, and 23rd rolls, then your first four data points would be (1,7), (2,10), (3,15), and (4,23).
Calculate the trendline equation for your data:
xy
 1 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
10 

Bonus question: If you were to continue tracking points for the first 1000 rolls, what would you predict the slope of the trendline to be? Do you have any intuition as to why?

Once completed, this page to a pdf document; then hand it in through your course's Learning Management System.

 Neil Simonetti

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