b) Compute the Correlation Coefficient for your line from (a). c) Using your answer to (b), Is there a Correlation between the variables at the a = 0.01 level of significance? Why?

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2. My Uncle is a bit of a conspiracy theorist-he is convinced that the number of UFO sightings
are on the rise in lowa. He dug through recently declassified FBI files and sorted them by
decades-he showed me the following data and wondered if I could use my "math
superpowers" to test it.
Years since 1900
(x)
Number of UFO Sightings in
lowa (y)
50
>y= 161
10
x = 560
60
>x? = 47600
25
= 4033
70
20
80
18
> xy = 13640
90
30
100
28
110
30
a) Compute the Equation of the Linear Regression Line between these variables.
Transcribed Image Text:2. My Uncle is a bit of a conspiracy theorist-he is convinced that the number of UFO sightings are on the rise in lowa. He dug through recently declassified FBI files and sorted them by decades-he showed me the following data and wondered if I could use my "math superpowers" to test it. Years since 1900 (x) Number of UFO Sightings in lowa (y) 50 >y= 161 10 x = 560 60 >x? = 47600 25 = 4033 70 20 80 18 > xy = 13640 90 30 100 28 110 30 a) Compute the Equation of the Linear Regression Line between these variables.
b) Compute the Correlation Coefficient for your line from (a).
c) Using your answer to (b), Is there a Correlation between the variables at the a = 0.01
level of significance? Why?
d) Using your answer to (c), predict the number of UFO visits in lowa in 1920.
e) I made you do all this because last year my Uncle found another set of data and made me
do this same thing-here is last year's data (x and y are defined identically) :
Linear Regression Equation : ŷ = -0.97 + 0.031x
Number of Data Pairs : 15
y = 16
Correlation Coefficient : 0.668
Using this model, determine if there is a correlation at the a = 0.01 level of significance, then
predict the number of UFO visits in lowa in 1920.
f) Based on your answers to parts (d) and (e), which prediction is more believable in reality?
Explain.
Transcribed Image Text:b) Compute the Correlation Coefficient for your line from (a). c) Using your answer to (b), Is there a Correlation between the variables at the a = 0.01 level of significance? Why? d) Using your answer to (c), predict the number of UFO visits in lowa in 1920. e) I made you do all this because last year my Uncle found another set of data and made me do this same thing-here is last year's data (x and y are defined identically) : Linear Regression Equation : ŷ = -0.97 + 0.031x Number of Data Pairs : 15 y = 16 Correlation Coefficient : 0.668 Using this model, determine if there is a correlation at the a = 0.01 level of significance, then predict the number of UFO visits in lowa in 1920. f) Based on your answers to parts (d) and (e), which prediction is more believable in reality? Explain.
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