Match the name of the shape to its word description:

What is the value of the correlation coefficient r of the data set?

enyata [817]

The correct option will be: C) 0.84

Explanation

Formula for Correlation coefficient :

$r= \frac{n(\Sigma xy)-(\Sigma x)(\Sigma y)}{\sqrt{[n\Sigma x^2-(\Sigma x)^2][n\Sigma y^2-(\Sigma y)^2]}}$

First, for each point(x, y), we need to calculate x², y² and xy .

Then, we will find sum all x, y, x², y² and xy, which gives us Σx, Σy, Σx², ∑y² and Σxy

(Please refer to the attached image for the table )

Here we got, ∑x = 44 , ∑y = 183 , ∑x² = 362 , ∑y² = 6575 and ∑xy = 1480

'n' is the total number of data set, which is 7 here.

So, plugging those values into the above formula..........

$r= \frac{n(\Sigma xy)-(\Sigma x)(\Sigma y)}{\sqrt{[n\Sigma x^2-(\Sigma x)^2][n\Sigma y^2-(\Sigma y)^2]}}\\ \\ r=\frac{7(1480)-(44)(183)}{\sqrt{[7(362)-(44)^2][7(6575)-(183)^2]}}\\ \\ r=\frac{10360-8052}{\sqrt{(598)(12536)}}\\ \\ r=\frac{2308}{\sqrt{7496528}}\\ \\ r=0.84$

So, the value of the correlation coefficient is 0.84

4 0

2 years ago

Read 2 more answers

Which ratio is not equivalent to -(1/3) (#6)

LuckyWell [14K]

Answer:

answer b

Step-by-step explanation:

hope that helps

7 0

2 years ago

What is the domain and range of the function y = 2x2 - 4x - 10?

11111nata11111 [884]

Answer:

Step-by-step explanation:

The domain of all polynomials is all real numbers. To find the range, let's solve that quadratic for its vertex. We will do this by completing the square. To begin, set the quadratic equal to 0 and then move the -10 over by addition. The first rule is that the leading coefficient has to be a 1; ours is a 2 so we factor it out. That gives us:

$2(x^2-2x)=10$

The second rule is to take half the linear term, square it, and add it to both sides. Our linear term is 2 (from the -2x). Half of 2 is 1, and 1 squared is 1. So we add 1 into the parenthesis on the left. BUT we cannot ignore the 2 sitting out front of the parenthesis. It is a multiplier. That means that we didn't just add in a 1, we added in a 2 * 1 = 2. So we add 2 to the right as well, giving us now:

$2(x^2-2x+1)=10+2$

The reason we complete the square (other than as a means of factoring) is to get a quadratic into vertex form. Completing the square gives us a perfect square binomial on the left.

$x^2-2x+1=(x-1)^2$ and on the right we will just add 10 and 2:

$2(x-1)^2=12$

Now we move the 12 back over by subtracting and set the quadratic back to equal y:

$2(x-1)^2-12=y$

From this vertex form we can see that the vertex of the parabola sits at (1,-12). This tells us that the absolute lowest point of the parabola (since it is positive it opens upwards) is -12. Therefore, the range is R={y|y ≥ -12}

4 0

3 years ago

Find two unit vectos that are orthogonal to both [0,1,2] and [1,-2,3]

alekssr [168]

Answer:

Let the vectors be

a = [0, 1, 2] and

b = [1, -2, 3]

( 1 ) The cross product of a and b (a x b) is the vector that is perpendicular (orthogonal) to a and b.

Let the cross product be another vector c.

To find the cross product (c) of a and b, we have

$\left[\begin{array}{ccc}i&j&k\\0&1&2\\1&-2&3\end{array}\right]$