Respuesta :
Answer:
[tex] \sum x= 37, \sum y= 672, \sum xy =2907, \sum x^2 =173, \sum y^2 = 51320[/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]
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}=173-\frac{37^2}{9}=20.889[/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}}=2907-\frac{37*672}{9}=144.333[/tex]
And the slope would be:
[tex]m=\frac{144.333}{20.889}=6.90953[/tex]
Nowe we can find the means for x and y like this:
[tex]\bar x= \frac{\sum x_i}{n}=\frac{37}{9}=4.111[/tex]
[tex]\bar y= \frac{\sum y_i}{n}=\frac{672}{9}=74.667[/tex]
And we can find the intercept using this:
[tex]b=\bar y -m \bar x=74.667-(6.9096*4.111)=46.241[/tex]
So the line would be given by:
[tex]y=6.9096 x +46.241[/tex]
And for this case the value of the slope m = 6.9096 means that for every increase of 1 unit in the number of years we have an increase of approximately 6.9096 in the grades of the test.
Step-by-step explanation:
Data given:
x: 3, 4, 4, 5, 3, 6, 2, 7, 3
y: 61, 68, 75, 82, 73, 90, 58, 93, 72
[tex]m=\frac{S_{xy}}{S_{xx}}[/tex]
[tex] \sum x= 37, \sum y= 672, \sum xy =2907, \sum x^2 =173, \sum y^2 = 51320[/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]
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}=173-\frac{37^2}{9}=20.889[/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}}=2907-\frac{37*672}{9}=144.333[/tex]
And the slope would be:
[tex]m=\frac{144.333}{20.889}=6.90953[/tex]
Nowe we can find the means for x and y like this:
[tex]\bar x= \frac{\sum x_i}{n}=\frac{37}{9}=4.111[/tex]
[tex]\bar y= \frac{\sum y_i}{n}=\frac{672}{9}=74.667[/tex]
And we can find the intercept using this:
[tex]b=\bar y -m \bar x=74.667-(6.9096*4.111)=46.241[/tex]
So the line would be given by:
[tex]y=6.9096 x +46.241[/tex]
And for this case the value of the slope m = 6.9096 means that for every increase of 1 unit in the number of years we have an increase of approximately 6.9096 in the grades of the test.
