Answer:
r = 0.9825; good correlation.
Step-by-step explanation:
One formula for the correlation coefficient is
![r = \dfrac{n\sum{xy} - \sum{x} \sum{y}}{\sqrt{n\left [\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [\sum{y}^{2}-\left (\sum{y}\right )^{2}\right]}}](https://tex.z-dn.net/?f=r%20%3D%20%5Cdfrac%7Bn%5Csum%7Bxy%7D%20-%20%5Csum%7Bx%7D%20%5Csum%7By%7D%7D%7B%5Csqrt%7Bn%5Cleft%20%5B%5Csum%7Bx%7D%5E%7B2%7D-%5Cleft%20%28%5Csum%7Bx%7D%5Cright%20%29%5E%7B2%7D%5Cright%5D%5Cleft%20%5B%5Csum%7By%7D%5E%7B2%7D-%5Cleft%20%28%5Csum%7By%7D%5Cright%20%29%5E%7B2%7D%5Cright%5D%7D%7D)
The calculation is not difficult, but it is tedious.
1. Calculate the intermediate numbers
We can display them in a table.
<u> </u><u>x</u> <u> y </u> <u> xy </u> <u> x² </u> <u> y² </u>
-3 -40 120 9 1600
1 12 12 1 144
5 72 360 25 5184
<u> 7</u> <u>137</u> <u> 959</u> <u>49</u> <u>18769
</u>
Σ = 10 181 1451 84 25697
2. Calculate the correlation coefficient
![r = \dfrac{n\sum{xy} - \sum{x} \sum{y}}{\sqrt{\left [n\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [n\sum{y}^{2}-\left (\sum{y}\right )^{2}\right]}}\\\\= \dfrac{4\times 1451 - 10\times 181}{\sqrt{[4\times 84 - 10^{2}][4\times25697 - 181^{2}]}}\\\\= \dfrac{5804 - 1810}{\sqrt{[336 - 100][102788 - 32761]}}\\\\= \dfrac{3994}{\sqrt{236\times70027}}\\\\= \dfrac{3994}{\sqrt{16526372}}\\\\= \dfrac{3994}{4065}\\\\= \mathbf{0.9825}](https://tex.z-dn.net/?f=r%20%3D%20%5Cdfrac%7Bn%5Csum%7Bxy%7D%20-%20%5Csum%7Bx%7D%20%5Csum%7By%7D%7D%7B%5Csqrt%7B%5Cleft%20%5Bn%5Csum%7Bx%7D%5E%7B2%7D-%5Cleft%20%28%5Csum%7Bx%7D%5Cright%20%29%5E%7B2%7D%5Cright%5D%5Cleft%20%5Bn%5Csum%7By%7D%5E%7B2%7D-%5Cleft%20%28%5Csum%7By%7D%5Cright%20%29%5E%7B2%7D%5Cright%5D%7D%7D%5C%5C%5C%5C%3D%20%5Cdfrac%7B4%5Ctimes%201451%20-%2010%5Ctimes%20181%7D%7B%5Csqrt%7B%5B4%5Ctimes%2084%20-%2010%5E%7B2%7D%5D%5B4%5Ctimes25697%20-%20181%5E%7B2%7D%5D%7D%7D%5C%5C%5C%5C%3D%20%5Cdfrac%7B5804%20-%201810%7D%7B%5Csqrt%7B%5B336%20-%20100%5D%5B102788%20-%2032761%5D%7D%7D%5C%5C%5C%5C%3D%20%5Cdfrac%7B3994%7D%7B%5Csqrt%7B236%5Ctimes70027%7D%7D%5C%5C%5C%5C%3D%20%5Cdfrac%7B3994%7D%7B%5Csqrt%7B16526372%7D%7D%5C%5C%5C%5C%3D%20%5Cdfrac%7B3994%7D%7B4065%7D%5C%5C%5C%5C%3D%20%5Cmathbf%7B0.9825%7D)
The closer the value of r is to +1 or -1, the better the correlation is. The values of x and y are highly correlated.
<span>Given the
table that shows the hair lengths y (in inches) of your friend and her cousin in different months x.
Month Friends Hair(in) Cousins Hair(in)
3 4 7
8 6.5 9.
To solve for the
cousins hair, recall that the equation of a line is given by
y = mx + c
From the table,
7 = 3m + c . . . (1)
9 = 8m + c . . . (2)
(1) - (2) ⇒ -2 = -5m
Substituting for m into equation (1) gives:
Therefore, the equation representing the growth of the cousin's hair is given by y = 1.2x + 5.8
</span>
Given:
standard deviation = 4.3%
sample size = 15
mean = 26.4%
error = σ/√n
error = 4.3% / √15
error = 4.3% / 3.873
error = 0.0111
0.0111 x 100% = 1.11%
Answer:
52 tickets cost $10 and 18 tickets cost $12
Step-by-step explanation:
10x+12y=804. (1)
x+y=70. (2)
From (2)
x=70-y
Substitute x=70-y into (1)
10x+12y=804
10(70-y)+12y=804
700-10y+12y=804
700+2y=804
2y=804-700
2y=104
y=104/2
y=52
Recall
x+y=70
x+52=70
x=70-52
x=18
52 tickets cost $10 and 18 tickets cost $12
When will he have less than 40 wheels left? Well you can make the equation...
85-4x=40
And then solve for x.
85-4x=40
-4x=-45
x=11 1/4 rounded up to 12
answer: He will have less than 40 wheels left after he has built 12 cars.
