Respuesta :
Answer:
[tex]\sum_{i=1}^n x_i =459[/tex]
[tex]\sum_{i=1}^n y_i =1227[/tex]
[tex]\sum_{i=1}^n x^2_i =24059[/tex]
[tex]\sum_{i=1}^n y^2_i =168843[/tex]
[tex]\sum_{i=1}^n x_i y_i =63544[/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}=24059-\frac{459^2}{9}=650[/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}=63544-\frac{459*1227}{9}=967[/tex]
And the slope would be:
[tex]m=\frac{967}{650}=1.488[/tex]
Nowe we can find the means for x and y like this:
[tex]\bar x= \frac{\sum x_i}{n}=\frac{459}{9}=51[/tex]
[tex]\bar y= \frac{\sum y_i}{n}=\frac{1227}{9}=136.33[/tex]
And we can find the intercept using this:
[tex]b=\bar y -m \bar x=136.33-(1.488*51)=60.442[/tex]
So the line would be given by:
[tex]y=1.488 x +60.442[/tex]
And then the best predicted value of y for x = 41 is:
[tex]y=1.488*41 +60.442 =121.45[/tex]
Step-by-step explanation:
For this case we assume the following dataset given:
x: 38,41,45,48,51,53,57,61,65
y: 116,120,123,131,142,145,148,150,152
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 =459[/tex]
[tex]\sum_{i=1}^n y_i =1227[/tex]
[tex]\sum_{i=1}^n x^2_i =24059[/tex]
[tex]\sum_{i=1}^n y^2_i =168843[/tex]
[tex]\sum_{i=1}^n x_i y_i =63544[/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}=24059-\frac{459^2}{9}=650[/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}=63544-\frac{459*1227}{9}=967[/tex]
And the slope would be:
[tex]m=\frac{967}{650}=1.488[/tex]
Nowe we can find the means for x and y like this:
[tex]\bar x= \frac{\sum x_i}{n}=\frac{459}{9}=51[/tex]
[tex]\bar y= \frac{\sum y_i}{n}=\frac{1227}{9}=136.33[/tex]
And we can find the intercept using this:
[tex]b=\bar y -m \bar x=136.33-(1.488*51)=60.442[/tex]
So the line would be given by:
[tex]y=1.488 x +60.442[/tex]
And then the best predicted value of y for x = 41 is:
[tex]y=1.488*41 +60.442 =121.45[/tex]
