Respuesta :
Answer:
[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=19616-\frac{342^2}{6}=122[/tex]
[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}=1142.2-\frac{342*19.9}{6}=7.9[/tex]
And the slope would be:
[tex]m=\frac{7.9}{122}=0.0648[/tex]
Nowe we can find the means for x and y like this:
[tex]\bar x= \frac{\sum x_i}{n}=\frac{342}{6}=57[/tex]
[tex]\bar y= \frac{\sum y_i}{n}=\frac{19.9}{6}=3.317[/tex]
And we can find the intercept using this:
[tex]b=\bar y -m \bar x=3.317-(0.0648*57)=-0.377[/tex]
So the line would be given by:
[tex]y=0.0648 x -0.377[/tex]
Explanation:
The data given is:
x: 60, 55, 62, 55,49, 61
y: 4.0, 3.2, 3.7, 3.9, 2.4, 2.7
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]
So we can find the sums like this:
[tex]\sum_{i=1}^n x_i = 342[/tex]
[tex]\sum_{i=1}^n y_i =19.9[/tex]
[tex]\sum_{i=1}^n x^2_i =19616[/tex]
[tex]\sum_{i=1}^n y^2_i =68.19[/tex]
[tex]\sum_{i=1}^n x_i y_i =1142.2[/tex]
With these we can find the sums:
[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=19616-\frac{342^2}{6}=122[/tex]
[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}=1142.2-\frac{342*19.9}{6}=7.9[/tex]
And the slope would be:
[tex]m=\frac{7.9}{122}=0.0648[/tex]
Nowe we can find the means for x and y like this:
[tex]\bar x= \frac{\sum x_i}{n}=\frac{342}{6}=57[/tex]
[tex]\bar y= \frac{\sum y_i}{n}=\frac{19.9}{6}=3.317[/tex]
And we can find the intercept using this:
[tex]b=\bar y -m \bar x=3.317-(0.0648*57)=-0.377[/tex]
So the line would be given by:
[tex]y=0.0648 x -0.377[/tex]
