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Consider the following sample data: x 14 16 17 18 20 y 20 14 17 12...

Consider the following sample data:

x 14 16 17 18 20
y 20 14 17 12 13

a. Calculate the covariance between the variables. (Negative value should be indicated by a minus sign. Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

b. Calculate the correlation coefficient. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

math   Statistics-And-Probability   
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Answer #1

Solution:-

a.

No.of Inputs 5
X Mean 17
Y Mean 15.2
Covariance(X,Y) -5.75
Calculation

Sum(X) = 14 + 16 + 17 + 18 + 20 = 85
XMean = 17
Sum(Y) = 20 + 14 + 17 + 12 + 13 = 76
YMean = 15.2
Covariance(X,Y) = SUM(xi - xmean)*(yi - ymean)/(samplesize -1)
= (14-17)*(20-15.2)+(16-17)*(14-15.2)+(17-17)*(17-15.2)+(18-17)*(12-15.2)+(20-17)*(13-15.2))/4
= -5.75

b.  correlation coefficient r = -0.79

The corelation coefficient is: r= 0.7861 Explanation Step 1: Find x.y. X aY2 as it was done in the table below 14 20 280 198 256 289 400 196 289 144 169 16 14 289 216 260 18 12 20 13 400 Step 2: Find the sum of every column to get: Step 3: Use the following formula to work out the correlation coefficient. 5-1269-85 7 -0.7861 5.1465 -855-1198-76

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