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Verdich [7]
3 years ago
9

Please consider the following values for the variables X and Y. Treat each row as a pair of scores for the variables X and Y (wi

th the first row providing the labels "X" and "Y"). X Y 2 4 4 3 6 5 7 7 11 6 Please calculate Pearson's correlation coefficient (r) for these data and report your answer below. When reporting your answer, please provide three decimal places (if relevant).

Mathematics
1 answer:
Studentka2010 [4]3 years ago
5 0

Answer:

The Pearson's coefficient of correlation between the is 0.700.

Step-by-step explanation:

The correlation coefficient is a statistical degree that computes the strength of the linear relationship amid the relative movements of the two variables (i.e. dependent and independent).It ranges from -1 to +1.

The formula to compute correlation between two variables <em>X</em> and <em>Y</em> is:

r(X, Y)=\frac{Cov(X, Y)}{\sqrt{V(X)\cdot V(Y)}}

The formula to compute covariance is:

Cov(X, Y)=n\cdot \sum XY-\sum X \cdot\sum Y

The formula to compute the variances are:

V(X)=n\cdot\sum X^{2}-(\sum X)^{2}\\V(Y)=n\cdot\sum Y^{2}-(\sum Y)^{2}

Consider the table attached below.

Compute the covariance as follows:

Cov(X, Y)=n\cdot \sum XY-\sum X \cdot\sum Y

                 =(5\times 165)-(30\times 25)\\=75

Thus, the covariance is 75.

Compute the variance of X and Y as follows:

V(X)=n\cdot\sum X^{2}-(\sum X)^{2}\\=(5\times 226)-(30)^{2}\\=230\\\\V(Y)=n\cdot\sum Y^{2}-(\sum Y)^{2}\\=(5\times 135)-(25)^{2}\\=50

Compute the correlation coefficient as follows:

r(X, Y)=\frac{Cov(X, Y)}{\sqrt{V(X)\cdot V(Y)}}

            =\frac{75}{\sqrt{230\times 50}}

            =0.69937\\\approx0.70

Thus, the Pearson's coefficient of correlation between the is 0.700.

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Step-by-step explanation:

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Laura takes very good care of her vehicles. She owns a blue van and a red truck. Although she bought them both new, she has owned the truck for 17 years longer than she has owned the van. If the sum of the ages of the vehicles is 41 years, how old is the van and how old is the truck?

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