This document summarizes a presentation about using regression analysis to predict the number of UFO sightings reported in each US state based on the state's population. It describes exploring the relationship between UFO sightings and population in a scatterplot, finding the regression line that best models their relationship, and using the line to estimate the number of UFO sightings based on a state's population. The regression analysis found that as state population increases, the number of reported UFO sightings also tends to increase and estimated the regression line relating the two variables.

1. Predicting UFO Sightings by State Population
Using Regression Analysis and R
Dr. Chantal Larose
Statistics and Data Analytics
School of Business
SUNY New Paltz
Digital Spaces Unconference 2016

2. Data Exploration
0200040006000
Reported UFO Sightings by Population
2006 Population (in Thousands)
UFOSightings
0 5000 10000 15000 20000 25000 30000 35000
As population increases, UFO sightings tend to increase. Not surprising.
larosec@newpaltz.edu Predicting UFO Sightings by State Population 1

3. Build Regression Line
Quantify the pattern between UFO sightings and population.
Describe the trend using a straight line:
Y = β0 + β1 × X +
Y = Reported UFO sightings
X = State Population
= Random error that makes the data not lay on the line
larosec@newpaltz.edu Predicting UFO Sightings by State Population 2

4. Build Regression Line
How to find β0 and β1? Use data to estimate them.
ˆβ1 = b1 =
n
i=1
(Xi − ¯X)(Yi − ¯Y )
n
i=1
(Xi − ¯X)2
ˆβ0 = b0 = ¯Y − b1 × ¯X
larosec@newpaltz.edu Predicting UFO Sightings by State Population 3

5. Using R (www.r-project.org)
R Code:
Results:
Regression Line:
Estimated UFO Sightings =
159.15 + 0.146 × (Thousand Population)
larosec@newpaltz.edu Predicting UFO Sightings by State Population 4

6. Data Exploration
0200040006000
Reported UFO Sightings by Population
2006 Population (in Thousands)
UFOSightings
0 5000 10000 15000 20000 25000 30000 35000
UFOs are reported more often in certain states than others!
larosec@newpaltz.edu Predicting UFO Sightings by State Population 5

7. Data Exploration
0200040006000
Reported UFO Sightings by Population
2006 Population (in Thousands)
UFOSightings
0 5000 10000 15000 20000 25000 30000 35000
California
Texas
Utah
Wisconsin
Californians are quicker to blame strange happenings on UFOs?
Texans more pragmatic?
larosec@newpaltz.edu Predicting UFO Sightings by State Population 6

8. Thank you!1
Thank you!
1Extracted from: Discovering Statistics, 3rd Edition. Daniel T. Larose. W. H. Freeman, 2016.
larosec@newpaltz.edu Predicting UFO Sightings by State Population 7