Respuesta :
Answer:
[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex]
For this case the value of r = -0.66
Now we can calculate the determination coeffcient:
[tex] r^2 = (-0.66)^2 = 0.4356[/tex]
And then we can conclude that 43.56% of the variation in y can be explained by the explanatory variable
And then 100-43.56 = 56.44 % of the variation in y that cannot be explained by the explanatory variable
Step-by-step explanation:
For this case we need to calculate the slope with the following formula:
[tex]m=\frac{S_{xy}}{S_{xx}}[/tex]
Where:
[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}[/tex]
[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}[/tex]
[tex]\bar x= \frac{\sum x_i}{n}[/tex]
[tex]\bar y= \frac{\sum y_i}{n}[/tex]
And we can find the intercept using this:
[tex]b=\bar y -m \bar x[/tex]
And the model obtained for this case is:
[tex] y = -3.4 +5.2 x[/tex]
The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.
And in order to calculate the correlation coefficient we can use this formula:
[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex]
For this case the value of r = -0.66
Now we can calculate the determination coeffcient:
[tex] r^2 = (-0.66)^2 = 0.4356[/tex]
And then we can conclude that 43.56% of the variation in y can be explained by the explanatory variable
And then 100-43.56 = 56.44 % of the variation in y that cannot be explained by the explanatory variable
The Coefficient of determination gives the proportion of variation which can be explained by the regression line.
The proportion of variation that cannot be explained by the given regression line is 56.44%
From the question, the correlation Coefficient, R = - 0.66
- The Coefficient of determination, R² can be calculated from the R value given.
- R² = - 0.66² = 0.4356
This means that :
- Percentage of variation that can be explained = (0.4356) × 100% = 43.56%
- The percentage of variation that cannot be explained = 100% - 43.56% = 56.44%
Therefore, proportion of the variation in y that cannot be explained is 56.44%
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