Respuesta :
Answer:
[tex]\sum_{i=1}^n x_i = 334[/tex]
[tex]\sum_{i=1}^n y_i =611[/tex]
[tex]\sum_{i=1}^n x^2_i =13970[/tex]
[tex]\sum_{i=1}^n y^2_i =51581[/tex]
[tex]\sum_{i=1}^n x_i y_i =26584[/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}=13970-\frac{334^2}{10}=2814.4[/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}=26584-\frac{334*611}{10}=6176.6[/tex]
And the slope would be:
[tex]m=\frac{6176.6}{2814.4}=2.195[/tex]
Nowe we can find the means for x and y like this:
[tex]\bar x= \frac{\sum x_i}{n}=\frac{334}{10}=33.4[/tex]
[tex]\bar y= \frac{\sum y_i}{n}=\frac{611}{10}=61.1[/tex]
And we can find the intercept using this:
[tex]b=\bar y -m \bar x=61.1-(2.195*33.4)=-12.213[/tex]
So the line would be given by:
[tex]y=2.195 x -12.213[/tex]
Step-by-step explanation:
The data given on this case is:
x: 14,12,20,16,46,23,48,50,55,50
y: 24,24,28,30,80,30,90,85,120,110
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 = 334[/tex]
[tex]\sum_{i=1}^n y_i =611[/tex]
[tex]\sum_{i=1}^n x^2_i =13970[/tex]
[tex]\sum_{i=1}^n y^2_i =51581[/tex]
[tex]\sum_{i=1}^n x_i y_i =26584[/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}=13970-\frac{334^2}{10}=2814.4[/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}=26584-\frac{334*611}{10}=6176.6[/tex]
And the slope would be:
[tex]m=\frac{6176.6}{2814.4}=2.195[/tex]
Nowe we can find the means for x and y like this:
[tex]\bar x= \frac{\sum x_i}{n}=\frac{334}{10}=33.4[/tex]
[tex]\bar y= \frac{\sum y_i}{n}=\frac{611}{10}=61.1[/tex]
And we can find the intercept using this:
[tex]b=\bar y -m \bar x=61.1-(2.195*33.4)=-12.213[/tex]
So the line would be given by:
[tex]y=2.195 x -12.213[/tex]
Answer:
The regression equation of the line is [tex]y=2.39x+0.765[/tex]
Step-by-step explanation:
Given:
The X column indicates the number of client contacts last month and the Y column shows the value of sales ($ thousands) last month for each client sampled.
[tex]x: 14,12,20,16,46,23,48,50,55,50\\y: 24,24,28,30,80,30,90,85,120,110[/tex]
Solution:
The expression for finding the slope for the above cases is formulated below,
[tex]m=\dfrac{S_{xy}}{S{xx}}[/tex]
Where,
[tex]S_{xy}=\sum\limits_{{i=1}}^{{n}}{{x_iy_i-\dfrac{\sum\limits_{{i=1}}^{{n}}{{x_i\sum\limits_{{i=1}}^{{n}}{{y_i}} }} }{n}}}[/tex]
[tex]S_{xx}=\sum\limits_{{i=1}}^{{n}}{{x_i^2-\dfrac{\left[\sum\limits_{{i=1}}^{{n}}x_i\right]^2}{n}[/tex]
Therefore,
[tex]x^2: 196,144,400,256,2116,529,2304,2500,3025,2500\\y^2: 576,576,784,900,6400,900,8100,7225,14400,12100[/tex]
[tex]xy: 336,288,560,480,3680,690,4320,4250,6600,5500[/tex]
Now, as per the given data,
[tex]\sum\limits_{i=1}^{n} x =334[/tex]
[tex]\sum\limits_{i=1}^{n} y =611[/tex]
[tex]\sum\limits_{i=1}^{n} x_i^2 =13970[/tex]
[tex]\sum\limits_{i=1}^{n} y_i^2 =51961[/tex]
[tex]\sum\limits_{i=1}^{n} x_iy_i =26704[/tex]
Therefore, plug-in these values in [tex]S_{xy}[/tex].
[tex]\begin{aligned}S_{xy}&=26704-\dfrac{334 \times 611}{10}\\&=26704-20407.4\\&=6296.6 \end{aligned}[/tex]
Similarly,
[tex]S_{xx}=13790-\dfrac{334^2}{10}\\=13790-11155.6\\=2634.4[/tex]
Hence,
[tex]\begin{aligned}m&=\dfrac{S_{xy}}{S{xx}}\\&=\dfrac{6296.6}{2634.4}\\&=2.39\end{aligned}[/tex]
Now, the points are extracted from the below formula,
x=334/10=33.4
y=611/10=61.1
Apply the slope-intercept form of the line,
[tex]y=mx+c\\y=2.39x+c[/tex]
The point (x,y) will satisfy the above equation,
thus,
[tex]61.1=2.39 \times 33.4+c\\0.765=c[/tex]
Plugin the value of c.
[tex]y=2.39x+0.765[/tex]
To know more, please refer to the link:
https://brainly.com/question/12820187?referrer=searchResults
