Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
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:
[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:
[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:
[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
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.
