Question
In: Statistics and Probability
Subject x y 1 16 25 2 14 31 3 10 16 4 5 18 5...
| Subject | x | y |
| 1 | 16 | 25 |
| 2 | 14 | 31 |
| 3 | 10 | 16 |
| 4 | 5 | 18 |
| 5 | 10 | 22 |
Find the linear correlation coefficient.
Solutions
Expert Solution
X: X Values
Y: Y Values
Mx: Mean of X Values
My: Mean of Y Values
X - Mx & Y - My: Deviation
scores
(X - Mx)2 & (Y -
My)2: Deviation Squared
(X - Mx)(Y - My): Product of
Deviation Scores
| x | y | X - Mx | Y - My | (X - Mx)2 | (Y - My)2 | (X - Mx)(Y - My) |
| 16 | 25 | 5 | 2.6 | 25 | 6.76 | 13 |
| 14 | 31 | 3 | 8.6 | 9 | 73.96 | 25.8 |
| 10 | 16 | -1 | -6.4 | 1 | 40.96 | 6.4 |
| 5 | 18 | -6 | -4.4 | 36 | 19.36 | 26.4 |
| 10 | 22 | -1 | -0.4 | 1 | 0.16 | 0.4 |
| Mx: 11.000 | My: 22.400 | Sum: 72.000 | Sum: 141.200 | Sum: 72.000 |
Result Details & Calculation
X Values
∑ = 55
Mean = 11
∑(X - Mx)2 = SSx = 72
Y Values
∑ = 112
Mean = 22.4
∑(Y - My)2 = SSy = 141.2
X and Y Combined
N = 5
∑(X - Mx)(Y - My) = 72
R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = 72 / √((72)(141.2)) = 0.7141
Meta Numerics (cross-check)
r = 0.7141
The value of R is 0.7141.
This is a moderate positive correlation, which means there is a tendency for high X variable scores go with high Y variable scores (and vice versa).
The value of R2, the coefficient of determination, is 0.5099.
orchestra answered 2 years agoRelated Solutions
year X Y 1 10% 15% 2 24% 25% 3 10% 14% 4 -17% -22% 5...
year
X
Y
1
10%
15%
2
24%
25%
3
10%
14%
4
-17%
-22%
5
105
16%
calculate the arithmetic average returns variance and standard
deviation
Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 14% 15% 16% 18%...
Periods
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
12%
14%
15%
16%
18%
20%
1
0.990
0.980
0.971
0.962
0.952
0.943
0.935
0.926
0.917
0.909
0.893
0.877
0.870
0.862
0.847
0.833
2
0.980
0.961
0.943
0.925
0.907
0.890
0.873
0.857
0.842
0.826
0.797
0.769
0.756
0.743
0.718
0.694
3
0.971
0.942
0.915
0.889
0.864
0.840
0.816
0.794
0.772
0.751
0.712
0.675
0.658
0.641
0.609
0.579
4
0.961
0.924
0.888
0.855
0.823
0.792
0.763
0.735
0.708
0.683
0.636...
Subject ID education memory 1 16 112 2 18 117 3 14 96 4 20 114...
Subject ID
education
memory
1
16
112
2
18
117
3
14
96
4
20
114
5
16
106
6
14
80
7
14
89
8
12
94
9
18
113
10
13
111
11
17
112
12
18
84
13
12
108
14
16
95
15
12
117
16
14
83
17
8
106
18
12
100
19
21
120
20
15
103
e. Explain the direction and strength of the relationship based
on the r. (2 points total:...
Subject ID education memory 1 16 112 2 18 117 3 14 96 4 20 114...
Subject ID
education
memory
1
16
112
2
18
117
3
14
96
4
20
114
5
16
106
6
14
80
7
14
89
8
12
94
9
18
113
10
13
111
11
17
112
12
18
84
13
12
108
14
16
95
15
12
117
16
14
83
17
8
106
18
12
100
19
21
120
20
15
103
e. Explain the direction and strength of the relationship based
on the r. (2 points total:...
Given: x y -5 1 -4 5 -3 4 -2 7 -1 10 0 8 1...
Given:
x
y
-5
1
-4
5
-3
4
-2
7
-1
10
0
8
1
9
2
13
3
14
4
13
5
18
What are the confidence limits (alpha = 0.05) for the true mean
value of Y when X = 3?
X 1 3 5 3 4 4 Y 2 5 4 3 4 6 A: Plot...
X
1
3
5
3
4
4
Y
2
5
4
3
4
6
A: Plot the date
B: find the line of best fit
C: determine ŷ AT x=3
D: Find r and r^2
E: explain r and r^2
Maximize p = x + 8y subject to x + y ≤ 25 y ≥ 10...
Maximize p = x + 8y subject to
x
+
y
≤
25
y
≥
10
2x
−
y
≥
0
x ≥ 0, y ≥ 0.
P=? (X,Y)= ? (NOT BY GRAPHING)
Week 1 2 3 4 5 6 Value 18 14 15 10 17 15 Using the...
Week
1
2
3
4
5
6
Value
18
14
15
10
17
15
Using the naïve method (most recent value) as the forecast for
the next week, compute the following measures of forecast
accuracy.
(a)
Mean absolute error
If required, round your answer to one decimal place.
(b)
Mean squared error
If required, round your answer to one decimal place.
(c)
Mean absolute percentage error
If required, round your intermediate calculations and final
answer to two decimal places.
(d)...
ID X Y 1 2 3 2 3 6 3 4 6 4 5 7 5...
ID
X
Y
1
2
3
2
3
6
3
4
6
4
5
7
5
8
7
6
5
7
7
6
7
8
8
8
9
7
8
10
12
11
Test the significance of the correlation coefficient.
Then use math test scores (X) to predict physics test scores
(Y). Do the following:
Create a scatterplot of X and Y.
Write the regression equation and interpret the regression
coefficients (i.e., intercept and slope).
Predict the physics score for each....
Given the following dataset x 1 1 2 3 4 5 y 0 2 4 5 ...
Given the following dataset x 1
1 2 3 4 5
y 0 2 4
5 5 3
We want to test the claim that there is a correlation between
xand y. The level of cretaine phosphokinase (CPK) in blood samples
measures the amount of muscle damage for athletes. At Jock State
University, the level of CPK was determined for each of 25 football
players and 15 soccer players before and after practice. The two
groups of athletes are trained...
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