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 X and Y is:
[tex]r(X, Y)=\frac{Cov(X, Y)}{\sqrt{V(X)\cdot V(Y)}}[/tex]
The formula to compute covariance is:
[tex]Cov(X, Y)=n\cdot \sum XY-\sum X \cdot\sum Y[/tex]
The formula to compute the variances are:
[tex]V(X)=n\cdot\sum X^{2}-(\sum X)^{2}\\V(Y)=n\cdot\sum Y^{2}-(\sum Y)^{2}[/tex]
Consider the table attached below.
Compute the covariance as follows:
[tex]Cov(X, Y)=n\cdot \sum XY-\sum X \cdot\sum Y[/tex]
[tex]=(5\times 165)-(30\times 25)\\=75[/tex]
Thus, the covariance is 75.
Compute the variance of X and Y as follows:
[tex]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[/tex]
Compute the correlation coefficient as follows:
[tex]r(X, Y)=\frac{Cov(X, Y)}{\sqrt{V(X)\cdot V(Y)}}[/tex]
[tex]=\frac{75}{\sqrt{230\times 50}}[/tex]
[tex]=0.69937\\\approx0.70[/tex]
Thus, the Pearson's coefficient of correlation between the is 0.700.
