Respuesta :
Answer:
[tex]m=\frac{27.75}{375}=0.074[/tex]
Nowe we can find the means for x and y like this:
[tex]\bar x= \frac{\sum x_i}{n}=\frac{150}{12}=12.5[/tex]
[tex]\bar y= \frac{\sum y_i}{n}=\frac{28.5}{12}=2.375[/tex]
And we can find the intercept using this:
[tex]b=\bar y -m \bar x=2.375-(0.074*12.5)=1.45[/tex]
So the line would be given by:
[tex]y=0.074 x +1.45[/tex]
C. = 1.45 + 0.074x
Step-by-step explanation:
The data given is:
x: 5,5,510,10,10, 15,15,15, 20,20,20
y: 1.6,2.2,1.4, 1.9, 2.4,2.6, 2.3,2.7, 2.8,2.6, 2.9, 3.1
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 = 150[/tex]
[tex]\sum_{i=1}^n y_i =28.5[/tex]
[tex]\sum_{i=1}^n x^2_i =2250[/tex]
[tex]\sum_{i=1}^n y^2_i =70.69[/tex]
[tex]\sum_{i=1}^n x_i y_i =384[/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}=2250-\frac{150^2}{12}=375[/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}=384-\frac{150*28.5}{12}=27.75[/tex]
And the slope would be:
[tex]m=\frac{27.75}{375}=0.074[/tex]
Nowe we can find the means for x and y like this:
[tex]\bar x= \frac{\sum x_i}{n}=\frac{150}{12}=12.5[/tex]
[tex]\bar y= \frac{\sum y_i}{n}=\frac{28.5}{12}=2.375[/tex]
And we can find the intercept using this:
[tex]b=\bar y -m \bar x=2.375-(0.074*12.5)=1.45[/tex]
So the line would be given by:
[tex]y=0.074 x +1.45[/tex]
C. = 1.45 + 0.074x
