Answer:
[tex]m=\frac{2506.833}{604.833}=4.1447[/tex]
Nowe we can find the means for x and y like this:
[tex]\bar x= \frac{\sum x_i}{n}=\frac{77}{6}=12.833[/tex]
[tex]\bar y= \frac{\sum y_i}{n}=\frac{587}{6}=97.833[/tex]
And we can find the intercept using this:
[tex]b=\bar y -m \bar x=97.833-(4.1447*12.833)=44.644[/tex]
So the line would be given by:
[tex]y=4.1447 x +44.644[/tex]
Step-by-step explanation:
[tex]m=\frac{S_{xy}}{S_{xx}}[/tex]
Σx = 77, Σy = 587, Σx2 = 1593, Σy2 = 70,533, and Σxy = 10040.
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}=1593-\frac{77^2}{6}=604.833[/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}}=10040-\frac{77*587}{6}=2506.833[/tex]
And the slope would be:
[tex]m=\frac{2506.833}{604.833}=4.1447[/tex]
Nowe we can find the means for x and y like this:
[tex]\bar x= \frac{\sum x_i}{n}=\frac{77}{6}=12.833[/tex]
[tex]\bar y= \frac{\sum y_i}{n}=\frac{587}{6}=97.833[/tex]
And we can find the intercept using this:
[tex]b=\bar y -m \bar x=97.833-(4.1447*12.833)=44.644[/tex]
So the line would be given by:
[tex]y=4.1447 x +44.644[/tex]
