Answer:
a) 
b) r =-0.932
The % of variation is given by the determination coefficient given by 
and on this case 
, so then the % of variation explained by the linear model is 86.87%.
Step-by-step explanation:
Assuming the following dataset:
Monthly Sales (Y) Interest Rate (X)
22 9.2
20 7.6
10 10.4
45 5.3
Part a
And we want a linear model on this way y=mx+b, where m represent the slope and b the intercept. In order to find the slope we have this formula:
Where:
With these we can find the sums:
And the slope would be:
Nowe we can find the means for x and y like this:
And we can find the intercept using this:
So the line would be given by:
Part b
For this case we need to calculate the correlation coefficient given by:
![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%3D%5Cfrac%7Bn%28%5Csum%20xy%29-%28%5Csum%20x%29%28%5Csum%20y%29%7D%7B%5Csqrt%7B%5Bn%5Csum%20x%5E2%20-%28%5Csum%20x%29%5E2%5D%5Bn%5Csum%20y%5E2%20-%28%5Csum%20y%29%5E2%5D%7D%7D)
![r=\frac{4(696.9)-(32.5)(97)}{\sqrt{[4(278.65) -(32.5)^2][4(3009) -(97)^2]}}=-0.937](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B4%28696.9%29-%2832.5%29%2897%29%7D%7B%5Csqrt%7B%5B4%28278.65%29%20-%2832.5%29%5E2%5D%5B4%283009%29%20-%2897%29%5E2%5D%7D%7D%3D-0.937)
So then the correlation coefficient would be r =-0.932
The % of variation is given by the determination coefficient given by and on this case , so then the % of variation explained by the linear model is 86.87%.
Given conditions are :
In 1980's, a typical middle-income household earned= $34,757
In 2009, a similar middle-income household earned= $38,550
And we have to find relative increase in income for these households from 1980 to 2009.
So first we will find the total increase in amounts.
Relative increase = 
= 10.91% or rounding it off we get approx 11%.
Hence, the answer is 11%.
Answer:
13.42
Step-by-step explanation:
65 sequences.
Lets solve the problem,
The last term is 0.
To form the first 18 terms, we must combine the following two sequences:
0-1 and 0-1-1
Any combination of these two sequences will yield a valid case in which no two 0's and no three 1's are adjacent
So we will combine identical 2-term sequences with identical 3-term sequences to yield a total of 18 terms, we get:
2x + 3y = 18
Case 1: x=9 and y=0
Number of ways to arrange 9 identical 2-term sequences = 1
Case 2: x=6 and y=2
Number of ways to arrange 6 identical 2-term sequences and 2 identical 3-term sequences =8!6!2!=28=8!6!2!=28
Case 3: x=3 and y=4
Number of ways to arrange 3 identical 2-term sequences and 4 identical 3-term sequences =7!3!4!=35=7!3!4!=35
Case 4: x=0 and y=6
Number of ways to arrange 6 identical 3-term sequences = 1
Total ways = Case 1 + Case 2 + Case 3 + Case 4 = 1 + 28 + 35 + 1 = 65
Hence the number of sequences are 65.
Learn more about Sequences on:
brainly.com/question/12246947
#SPJ4
Answer:
Parallel: y=-4x-1
Perpendicular: y=-4x+13/2
Step-by-step explanation:
For the equation y=-4x-41, the slope is -4. Writing a line related to this equation has two options:
- If the line will be parallel to it then this is the slope of the new line as well. Use the point-slope form to write the equation, then simplify and convert into the slope intercept form.
(y-7)=-4(x--2)
y-7=-4x-8
y=-4x-1
- If the line will be perpendicular to it then the slope is the negative reciprocal of the previous slope. It is 1/4.
(y-7)=1/4(x--2)
y-7=1/4x-1/2
y=-4x+13/2
