Answer:
D
Step-by-step explanation:
none of the others make sense
Answer:
42.1% of variation in the response is explained by the regression line
Step-by-step explanation:
Correlation coefficient is a measure which tells us that how strongly are two variables under study are linearly related to each other i.e correlation coefficient gives the strength of linear association between the variables.
If the magnitude of correlation coefficient is closer to 1, it indicates a strong linear relationship. If the magnitude of correlation coefficient is closer to 0, it indicates a weak linear relationship.
There is another variable known as "Coefficient of Determination", which is equal to square of Correlation Coefficient. Coefficient of Determination tells us that what percentage of variation in the response of the study can be explained by the regression line.
This means, for this question we need to calculate the Coefficient of Determination.
Correlation coefficient = r = 0.649
Coefficient of Determination = R = r² = (0.649)²= 0.421 = 42.1 %
This means that 42.1% of variation in the response is explained by the regression line.
Answer:
1) 
2) 
3) 
And the variance would be given by:
![Var (M)= E(M^2) -[E(M)]^2 = 207.1 -(13.9^2)= 13.89](https://tex.z-dn.net/?f=Var%20%28M%29%3D%20E%28M%5E2%29%20-%5BE%28M%29%5D%5E2%20%3D%20207.1%20-%2813.9%5E2%29%3D%2013.89)
And the deviation would be:
4) 
And the variance would be given by:
![Var (J)= E(J^2) -[E(J)]^2 = 194.8 -(11.8^2)= 55.56](https://tex.z-dn.net/?f=Var%20%28J%29%3D%20E%28J%5E2%29%20-%5BE%28J%29%5D%5E2%20%3D%20194.8%20-%2811.8%5E2%29%3D%2055.56)
And the deviation would be:
Step-by-step explanation:
For this case we have the following distributions given:
Probability M J
0.3 14% 22%
0.4 10% 4%
0.3 19% 12%
Part 1
The expected value is given by this formula:

And replacing we got:

Part 2

Part 3
We can calculate the second moment first with the following formula:

And the variance would be given by:
![Var (M)= E(M^2) -[E(M)]^2 = 207.1 -(13.9^2)= 13.89](https://tex.z-dn.net/?f=Var%20%28M%29%3D%20E%28M%5E2%29%20-%5BE%28M%29%5D%5E2%20%3D%20207.1%20-%2813.9%5E2%29%3D%2013.89)
And the deviation would be:
Part 4
We can calculate the second moment first with the following formula:

And the variance would be given by:
![Var (J)= E(J^2) -[E(J)]^2 = 194.8 -(11.8^2)= 55.56](https://tex.z-dn.net/?f=Var%20%28J%29%3D%20E%28J%5E2%29%20-%5BE%28J%29%5D%5E2%20%3D%20194.8%20-%2811.8%5E2%29%3D%2055.56)
And the deviation would be:
Answer:
12, 13, 14
Step-by-step explanation:
Denote the integers as:
x
x+1
x+2
The sum of their squares, so that would be;
(x^(2)) + (( x + 1 )^(2)) + (( x + 2 )^(2)) = 509
write out the squares
x^2 + x^2 + 2x + 1 + x^2 + 4x + 4 = 509
combine like terms
3x^2 + 6x + 5 = 509
inverse operations
3x^2 + 6x + 5 = 509
-5 -5
3x^2 + 6x = 504
factor
3x^2 + 6x = 504
3 ( x^2 + 2x ) =504
Inverse operations
3 ( x^2 + 2x ) = 504
/3 /3
x^2 + 2x = 168
Factor again
x ( x + 2 ) = 168
At this point, it should be obvious that x is 12 (because 12 * 14 = 168)
So now substitute back into the consecutive numbers
x = 12
x + 1 = 13
x + 2 = 14