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Answer :
The covariance value between two variables says, days to 230 lbs and backfat thickness, is 0.48..
The covariance value between any two variables is used to determine whether the variables are changing in the same direction. It relates the two variables if they are from different data sets.
Let X and Y be two data sets with different values. Then the covariance between X and Y is given by
Cov ( X,Y) = ∑ ( X ᵢ– u) ( Yⱼ-v ) /n
Where are Xᵢ's elements in the X data set
Yⱼ→ elements of the Y set
μ → mean of X data set
ν→ mean of Y set
n→ total number of observations
As we have given two sets of data, let days to 230 lbs and backfat thickness be sets X and Y, respectively.
Now, we shall calculate the mean value for X and Y sets.
Mean of X set = (164+158+180 + +160+198+172+186+178+178+186)/10= 176
The mean of Y set =
(1.0+ 1.1+ 1.2+ 1.4+1.2+1.3++1.1+1.3+1.4+1.0)/10 = 1.2
Xᵢ– μ - 12 -18 4 -16 22 -4 10 2 2 10
Yⱼ– ν -.2 - .1 0 .2 0 .1 -.1 .1 .2 -.2
(Xᵢ - μ)(Yⱼ- ν) 2.4 1.8 0 - 3.2. 0 0.4 1 4.4 -2
∑ (Xᵢ - μ ) ( Yⱼ - ν) = 4.8
put all the values of variables in above formula we get,. Cov( X, Y) = 4.8 / 10 = 0.48 ..
So, the Covariance between the days of 230lb and backfat thickness is 0.48 ..
To learn more about Covariance, refer :
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Rewritten by : Barada
The covariance between days to 230 lb and backfat thickness of a sample of 10 pigs is -0.444.
The student asked to calculate the covariance between days to 230 lb and backfat thickness for a sample of 10 pigs.
To find the covariance, follow these steps:
- Calculate the mean of both variables (days to 230 lb and backfat thickness).
- Subtract the mean from each data point to get the deviations.
- Multiply the deviations for corresponding data points.
- Sum these values.
- Divide by the number of observations minus one (n-1).
Given data:
- Days to 230 lb (X): 164, 180, 158, 160, 198, 172, 186, 178, 178, 186
- Backfat thickness (Y): 1.0, 1.1, 1.2, 1.4, 1.2, 1.3, 1.1, 1.3, 1.4, 1.0
Step-by-Step Calculation:
1. Calculate the means:
Mean of X: (164 + 180 + 158 + 160 + 198 + 172 + 186 + 178 + 178 + 186) / 10 = 176
Mean of Y: (1.0 + 1.1 + 1.2 + 1.4 + 1.2 + 1.3 + 1.1 + 1.3 + 1.4 + 1.0) / 10 = 1.20
2. Calculate deviations from the mean:
For X: -12, 4, -18, -16, 22, -4, 10, 2, 2, 10
For Y: -0.2, -0.1, 0.0, 0.2, 0.0, 0.1, -0.1, 0.1, 0.2, -0.2
3. Multiply the deviations:
-12 * -0.2, 4 * -0.1, -18 * 0.0, -16 * 0.2, 22 * 0.0, -4 * 0.1, 10 * -0.1, 2 * 0.1, 2 * 0.2, 10 * -0.2 = 2.4, -0.4, 0, -3.2, 0, -0.4, -1.0, 0.2, 0.4, -2.0
4. Sum the products:
2.4 - 0.4 + 0 - 3.2 + 0 - 0.4 - 1.0 + 0.2 + 0.4 - 2.0 = -4
5. Divide by n-1:
Covariance = -4 / (10-1) = -0.444
Therefore, the covariance between days to 230 lb and backfat thickness is -0.444.
