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iren2701 [21]
3 years ago
7

Elijah opened a checking account with​ $125 and deposits​ $25 into it every week. he opened another checking account with​ $225

and deposits​ $35 into it every week. write a simplified expression to represent how much he will have in both accounts after w weeks.
Business
1 answer:
kramer3 years ago
5 0
Bank account #1
25w + 125
Bank account #2
35w + 225
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a) $y=0.00991 x+1.042$b) $r^2=0.7503^2=0.563$\\C) $r=\frac{7(30095)-(4210)(49)}{\sqrt{\left[7(2595100)-(4210)^2\right]\left[7(354)-(49)^2\right]}}=0.7503$

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We want to create a linear model like this :

$$y=m x+b$$

Where

$$m=\frac{S_{x y}}{S_{x x}}$$

And:  

$$\begin{aligned}& S_{x y}=\sum_{i=1}^n x_i y_i-\frac{\left(\sum_{i=1}^n x_i\right)\left(\sum_{i=1}^n y_i\right)}{n} \\& S_{x x}=\sum_{i=1}^n x_i^2-\frac{\left(\sum_{i=1}^n x_i\right)^2}{n}\end{aligned}$$

With these we can find the sums:  

$$\begin{aligned}& S_{x x}=\sum_{i=1}^n x_i^2-\frac{\left(\sum_{i=1}^n x_i\right)^2}{n}=2595100-\frac{4210^2}{7}=63085.714 \\& S_{x y}=\sum_{i=1}^n x_i y_i-\frac{\left(\sum_{i=1}^n x_i\right)\left(\sum_{i=1}^n y_i\right) n}{=} 30095-\frac{4210 * 49}{7}=625\end{aligned}$$

And the slope would be:  

m=\frac{625}{63085.714}=0.00991

Now we can find the means for x and y like this:

$$\begin{aligned}& \bar{x}=\frac{\sum x_i}{n}=\frac{4210}{7}=601.429 \\& \bar{y}=\frac{\sum y_i}{n}=\frac{49}{7}=7\end{aligned}$$

And we can find the intercept using this:

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And the line would be:

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Part b

The correlation coefficient is given by:

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]}}

For our case we have this:

$$\begin{aligned}& \mathrm{n}=7 \sum x=4210, \sum y=49, \sum x y=30095, \sum x^2=2595100, \sum y^2=354 \\& r=\frac{7(30095)-(4210)(49)}{\sqrt{\left[7(2595100)-(4210)^2\right]\left[7(354)-(49)^2\right]}}=0.7503\end{aligned}$$

The determination coefficient is given by:

$$r^2=0.7503^2=0.563$$

Part c

r=\frac{7(30095)-(4210)(49)}{\sqrt{\left[7(2595100)-(4210)^2\right]\left[7(354)-(49)^2\right]}}=0.7503

Learn more about regression line to visit this link

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