Answer:
the correlation coefficient of the line of best fit is, 0.98247.
Step-by-step explanation:
Correlation Coefficient are used to find how strong relationship between the data. It expressed its values between +1 and -1. It is represented by r.
* if 0<r<1 indicates a strong positive relationship.
* -1<r <0 indicates a strong negative relationship.
* r=0 indicates no relationship at all.
The formula for this :
![r = \frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2-(\sum x)^2][n\sum y^2-(\sum y)^2]}}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7Bn%28%5Csum%20xy%29-%28%5Csum%20x%29%28%5Csum%20y%29%7D%7B%5Csqrt%7B%5Bn%5Csum%20x%5E2-%28%5Csum%20x%29%5E2%5D%5Bn%5Csum%20y%5E2-%28%5Csum%20y%29%5E2%5D%7D%7D)
Given the data: (-3, -40) , (1, 12), (5, 72) and (7,137)
Here, n = 4
To calculate the correlation coefficient r;
Substitute the values of data in above formla of r , as shown in the Figure 1:
then;
![r=\frac{4\cdot 1451-(10)(181)}{[4\cdot84-(10)^2][4\cdot 256977 -(181)^2]}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B4%5Ccdot%201451-%2810%29%28181%29%7D%7B%5B4%5Ccdot84-%2810%29%5E2%5D%5B4%5Ccdot%20256977%20-%28181%29%5E2%5D%7D)
or
![r=\frac{5804-1810}{\sqrt{[336-100][102788 -32761]}}=\frac{3994}{\sqrt{[236][70027]}}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B5804-1810%7D%7B%5Csqrt%7B%5B336-100%5D%5B102788%20-32761%5D%7D%7D%3D%5Cfrac%7B3994%7D%7B%5Csqrt%7B%5B236%5D%5B70027%5D%7D%7D)
or
Therefore, the correlation coefficient r is, 0.98247 (Positive relationship)
Answer:
In the explanation
Step-by-step explanation:
a) Multiply the second equation by 2, subtract both lines. You get x = -3. Plug this in to get y, y = -2
b) Multiply the first equation by 2, add both lines. You get x = 8. Plug this in to get y, y = -3
c) Multiply the first equation by 5, subtract both lines. You get y = 1. Plug this in to get x, x = -3
d) Multiply the first equation by 2 and the second one by 3, add both lines. You get x = 1. Plug this in to get y, y = 4
Hope this helps!
Answer:
5Y+8
Step-by-step explanation:
Proving a relation for all natural numbers involves proving it for n = 1 and showing that it holds for n + 1 if it is assumed that it is true for any n.
The relation 2+4+6+...+2n = n^2+n has to be proved.
If n = 1, the right hand side is equal to 2*1 = 2 and the left hand side is equal to 1^1 + 1 = 1 + 1 = 2
Assume that the relation holds for any value of n.
2 + 4 + 6 + ... + 2n + 2(n+1) = n^2 + n + 2(n + 1)
= n^2 + n + 2n + 2
= n^2 + 2n + 1 + n + 1
= (n + 1)^2 + (n + 1)
This shows that the given relation is true for n = 1 and if it is assumed to be true for n it is also true for n + 1.
<span>By mathematical induction the relation is true for any value of n.</span>
Answer:
(x - 2) (x - 12)
Step-by-step explanation:
Factor the following:
x^2 - 14 x + 24
The factors of 24 that sum to -14 are -2 and -12. So, x^2 - 14 x + 24 = (x - 2) (x - 12):
Answer: (x - 2) (x - 12)
