Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Get accurate and detailed answers to your questions from a dedicated community of experts on our Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
[tex]a) $y=0.00991 x+1.042$b) $r^2=0.7503^2=0.563$\\C) $r=\frac{7(30095)-(4210)(49)}{\sqrt{\left[7(2595100)-(4210)^2\right]\left[7(354)-(49)^2\right]}}=0.7503$[/tex]
x: 500, 700, 750, 590 , 540, 650, 480
y: 7.00, 7.50 , 9.00, 6.5, 7.50 , 7.0, 4.50
We want to create a linear model like this :
[tex]$y=m x+b$[/tex]
Where
[tex]$m=\frac{S_{x y}}{S_{x x}}$[/tex]
And: Â
[tex]$\begin{aligned}& S_{x y}=\sum_{i=1}^n x_i y_i-\frac{\left(\sum_{i=1}^n x_i\right)\left(\sum_{i=1}^n y_i\right)}{n} \\& S_{x x}=\sum_{i=1}^n x_i^2-\frac{\left(\sum_{i=1}^n x_i\right)^2}{n}\end{aligned}$[/tex]
With these we can find the sums: Â
[tex]$\begin{aligned}& S_{x x}=\sum_{i=1}^n x_i^2-\frac{\left(\sum_{i=1}^n x_i\right)^2}{n}=2595100-\frac{4210^2}{7}=63085.714 \\& S_{x y}=\sum_{i=1}^n x_i y_i-\frac{\left(\sum_{i=1}^n x_i\right)\left(\sum_{i=1}^n y_i\right) n}{=} 30095-\frac{4210 * 49}{7}=625\end{aligned}$[/tex]
And the slope would be: Â
[tex]m=\frac{625}{63085.714}=0.00991[/tex]
Now we can find the means for x and y like this:
[tex]$\begin{aligned}& \bar{x}=\frac{\sum x_i}{n}=\frac{4210}{7}=601.429 \\& \bar{y}=\frac{\sum y_i}{n}=\frac{49}{7}=7\end{aligned}$[/tex]
And we can find the intercept using this:
[tex]$b=\bar{y}-m \bar{x}=7-(0.00991 * 601.429)=1.042$[/tex]
And the line would be:
[tex]$y=0.00991 x+1.042$[/tex]
Part b
The correlation coefficient is given by:
[tex]r=\frac{n\left(\sum x y\right)-\left(\sum x\right)\left(\sum y\right)}{\sqrt{\left[n \sum x^2-\left(\sum x\right)^2\right]\left[n \sum y^2-\left(\sum y\right)^2\right]}}[/tex]
For our case we have this:
[tex]$\begin{aligned}& \mathrm{n}=7 \sum x=4210, \sum y=49, \sum x y=30095, \sum x^2=2595100, \sum y^2=354 \\& r=\frac{7(30095)-(4210)(49)}{\sqrt{\left[7(2595100)-(4210)^2\right]\left[7(354)-(49)^2\right]}}=0.7503\end{aligned}$[/tex]
The determination coefficient is given by:
[tex]$r^2=0.7503^2=0.563$[/tex]
Part c
[tex]r=\frac{7(30095)-(4210)(49)}{\sqrt{\left[7(2595100)-(4210)^2\right]\left[7(354)-(49)^2\right]}}=0.7503[/tex]
Learn more about regression line to visit this link
https://brainly.com/question/7656407
#SPJ4
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.
