Complete Question
The complete question is shown on the first uploaded image
Answer:
a
SST = 1800
SSR = 1512.376
SSE = 287.624
b
coefficient of determination is ![r^2 \approx 0.8402](https://tex.z-dn.net/?f=r%5E2%20%5Capprox%200.8402)
What this is telling us is that 84.02% variation in dependent variable y can be fully explained by variation in the independent variable x
c
The correlation coefficient is ![r = 0.917](https://tex.z-dn.net/?f=r%20%3D%200.917)
Step-by-step explanation:
The table shown the calculated mean is shown on the second uploaded image
Let first define some term
SST (sum of squares total) : This is the difference between the noted dependent variable and the mean of this noted dependent variable
SSR(sum of squared residuals) : this can defined as a predicted shift from the actual observed values of the data
SSE (sum of squared estimate of errors): this can be defined as the sum of the square difference between the observed value and its mean
From the table
![SST = SS_{yy} = 1800](https://tex.z-dn.net/?f=SST%20%3D%20SS_%7Byy%7D%20%3D%201800)
![SSR = \frac{SS^2_{xy}}{SS_{xx}} = \frac{4755^2}{14950} = 1512.376](https://tex.z-dn.net/?f=SSR%20%3D%20%5Cfrac%7BSS%5E2_%7Bxy%7D%7D%7BSS_%7Bxx%7D%7D%20%3D%20%5Cfrac%7B4755%5E2%7D%7B14950%7D%20%3D%201512.376)
![=1800 - 1512.376](https://tex.z-dn.net/?f=%3D1800%20-%201512.376)
![= 287.62](https://tex.z-dn.net/?f=%3D%20287.62)
The coefficient of determination is mathematically represented as
![r^2 = \frac{SSR}{SST}](https://tex.z-dn.net/?f=r%5E2%20%3D%20%5Cfrac%7BSSR%7D%7BSST%7D)
![= 1-\frac{SSE}{SST}](https://tex.z-dn.net/?f=%3D%201-%5Cfrac%7BSSE%7D%7BSST%7D)
![r^2= 1-\frac{287.6237}{1800}](https://tex.z-dn.net/?f=r%5E2%3D%201-%5Cfrac%7B287.6237%7D%7B1800%7D)
![r^2 \approx 0.8402](https://tex.z-dn.net/?f=r%5E2%20%5Capprox%200.8402)
The correlation coefficient is mathematically represented as
![r = \pm\sqrt{r^2}](https://tex.z-dn.net/?f=r%20%3D%20%5Cpm%5Csqrt%7Br%5E2%7D)
Substituting values
![r = \sqrt{0.84020}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%7B0.84020%7D)
![r = 0.917](https://tex.z-dn.net/?f=r%20%3D%200.917)
this value is + because the value of the coefficient of x in estimated regression equation(
) is positive
Answer:
True
Step-by-step explanation:
If there are an equal amount of red and blue marbles, then the statement would be true, since there's just as many red marbles in the jar as there are blue marbles.
Let's call the numbers x and y:
their sum is:
x+y=30
and their difference is x-y=12.
from the first equation: x=30-y
and we insert this into the second equation:
30-y-y=12.
we calculate:
30-2y=12
30-12=2y
18=2y
9=y
so the first number is 9 and the second is 30-9=21.
We have this square pyramid as shown in the picture. (Actually, a cross-section is a plane. So that, it is not fully drawn in the picture. You can see only part of it). It is given that EH⊥FG and we can easily observe that the cross-section is a triangle. It is a triangle Δ EFG.
we have the following:
![\begin{gathered} p=2\cdot l+2\cdot w \\ l=w+12 \\ p=160 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20p%3D2%5Ccdot%20l%2B2%5Ccdot%20w%20%5C%5C%20l%3Dw%2B12%20%5C%5C%20p%3D160%20%5Cend%7Bgathered%7D)
replacing:
![\begin{gathered} p=2\cdot(w+12)+2\cdot w \\ 160=2\cdot w+24+2\cdot w \\ 4\cdot w=160-24 \\ w=\frac{136}{4} \\ w=34 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20p%3D2%5Ccdot%28w%2B12%29%2B2%5Ccdot%20w%20%5C%5C%20160%3D2%5Ccdot%20w%2B24%2B2%5Ccdot%20w%20%5C%5C%204%5Ccdot%20w%3D160-24%20%5C%5C%20w%3D%5Cfrac%7B136%7D%7B4%7D%20%5C%5C%20w%3D34%20%5Cend%7Bgathered%7D)
therefore, the width is 34 feet, the length:
![\begin{gathered} l=34+12 \\ l=46 \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20l%3D34%2B12%20%5C%5C%20l%3D46%20%5C%5C%20%20%5Cend%7Bgathered%7D)
the length is 46 feet