Answer:
Step-by-step explanation:
Hello!
a.
Given the data corresponding the variables:
x 2 6 6 7 9
y 3 2 6 9 5
The Scatterplot is attached.
b.
To compute the correlation coefficient you need several auxiliary calculations:
∑X= 30
∑X²= 206
∑Y= 25
∑Y²= 155
∑XY= 162
![r= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{\sqrt{[sumX^2-\frac{(sumX)^2}{n} ][sumY^2-\frac{(sumY)^2}{n} ]} }](https://tex.z-dn.net/?f=r%3D%20%5Cfrac%7BsumXY-%5Cfrac%7B%28sumX%29%28sumY%29%7D%7Bn%7D%20%7D%7B%5Csqrt%7B%5BsumX%5E2-%5Cfrac%7B%28sumX%29%5E2%7D%7Bn%7D%20%5D%5BsumY%5E2-%5Cfrac%7B%28sumY%29%5E2%7D%7Bn%7D%20%5D%7D%20%7D)
![r= \frac{162-\frac{(30)*(25)}{5} }{\sqrt{[206-\frac{(30)^2}{5} ][155-\frac{(25)^2}{5} ]} }](https://tex.z-dn.net/?f=r%3D%20%5Cfrac%7B162-%5Cfrac%7B%2830%29%2A%2825%29%7D%7B5%7D%20%7D%7B%5Csqrt%7B%5B206-%5Cfrac%7B%2830%29%5E2%7D%7B5%7D%20%5D%5B155-%5Cfrac%7B%2825%29%5E2%7D%7B5%7D%20%5D%7D%20%7D)
r= 0.429 ≅ 0.43
c.
The critical value for r has n-2 degrees of freedom, let's say for example you have α:0.05
![r_{n-2;\alpha } = r_{3;0.05 } = 0.878](https://tex.z-dn.net/?f=r_%7Bn-2%3B%5Calpha%20%20%7D%20%3D%20r_%7B3%3B0.05%20%7D%20%3D%200.878)
For a two-tailed test.
Because the correlation coefficient is <u>positive</u> and the absolute value of the correlation coefficient, _<u>0.43</u>___, is <u>not greater</u> than the critical value for this data set,_<u>0.878</u>__, <u>no </u>linear relationship exists between x and y.
I hope it helps!
Answer:
-6/7
Step-by-step explanation:
So the question basically is asking, 6x7/15+x=8/7 so find the value of X.
We multiply 7/15 by six because the question says 6 7/15 and we multiply 8 by 1/7 to get 8/7. Hope that was useful!
Answer:
8
Step-by-step explanation:
Let's solve this problem step-by-step.
STEP-BY-STEP SOLUTION:
Let's first write down the equation we are going to solve.
( 1 / 3 )h - 4 [ ( 2 / 3 )h - 3 ] = ( 2 / 3 )h - 6
To begin with, we will expand the brackets => [ ]
( 1 / 3 )h - ( 8 / 3 )h + 12 = ( 2 / 3 )h - 6
Next we will collect like terms by placing all the individual numbers on the right-side of the equation and the terms with ( h ) on the left-hand side of the equation so that we can begin making ( h ) the subject.
( 1 / 3 )h - ( 8 / 3 )h - ( 2 / 3 )h = - 6 - 12
Then we will simplify both the left-hand side and right-hand side of the equation to solve it for ( h ).
( - 9 / 3 )h = - 18
- 3h = - 18
h = - 18 / - 3
h = 18 / 3
h = 6
FINAL ANSWER:
Therefore, the answer is:
h = 6
Hope this helps! :)
Have a lovely day! <3