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?
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd78dab7-ae13-48a1-821a-bf98ee472c72%2Fa07cf0a3-1d1d-445f-af3c-34f2491c742b%2F1gbimq5_processed.png&w=3840&q=75)
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd78dab7-ae13-48a1-821a-bf98ee472c72%2Fa07cf0a3-1d1d-445f-af3c-34f2491c742b%2F97hg1up_processed.png&w=3840&q=75)
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