1) Utilize the following information to calculate the requested information belo
ID: 3056162 • Letter: 1
Question
1)
Utilize the following information to calculate the requested information below to calculate a Pearson’s r. A researcher is interested in the relationship between the number of hours a student studies per week and their GPA. Use the information below to calculate the requested information. The researcher collected data from six students. (25 points)
Student
X (hours studying)
Y (GPA)
1
2
3
4
5
6
15
0
35
40
20
10
3.80
3.44
2.50
2.81
4.00
3.62
In the space below, write in the following: mean and standard deviation of X; mean and standard deviation of Y; the product of ZX*ZY for each student (labeled as “product for student 1, student 2, and so on); the Pearson’s r; interpretation of r (i.e., strength and direction of r); r2; and an interpretation of r2.
Student
X (hours studying)
Y (GPA)
1
2
3
4
5
6
15
0
35
40
20
10
3.80
3.44
2.50
2.81
4.00
3.62
Explanation / Answer
> x=c(15,0,35,40,20,10)
> y=c(3.8,3.44,2.5,2.81,4,3.62)
a)> mean(x)
[1] 20
> sd(x)
[1] 15.16575
b)> mean(y)
[1] 3.361667
> sd(y)
[1] 0.5863929
c)> x*y
[1] 57.0 0.0 87.5 112.4 80.0 36.2
d)> cor(x,y)
[1] -0.681428
The strength of relationship is quite strong and negative, i.e when x increases, y decreases and vice versa.
e)> cor(x,y)^2
[1] 0.4643441
This implies that if y is regressed upon x, 46.43% of the total variance will be explained by the regression model.
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