Is the following conditional true or false? If it is true, explain why. If it is false, give a counterexample

The least-squares regression model y =−3.4+5.2x and correlation coefficient r=−0.66 were calculated for a set of bivariate data

Makovka662 [10]

Answer:

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

For this case the value of r = -0.66

Now we can calculate the determination coeffcient:

$r^2 = (-0.66)^2 = 0.4356$

And then we can conclude that 43.56% of the variation in y can be explained by the explanatory variable

And then 100-43.56 = 56.44 % of the variation in y that cannot be explained by the explanatory variable

Step-by-step explanation:

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

$\bar x= \frac{\sum x_i}{n}$

$\bar y= \frac{\sum y_i}{n}$

And we can find the intercept using this:

$b=\bar y -m \bar x$

And the model obtained for this case is:

$y = -3.4 +5.2 x$

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:

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

For this case the value of r = -0.66

Now we can calculate the determination coeffcient:

$r^2 = (-0.66)^2 = 0.4356$

And then we can conclude that 43.56% of the variation in y can be explained by the explanatory variable

And then 100-43.56 = 56.44 % of the variation in y that cannot be explained by the explanatory variable

8 0

2 years ago

Anthony has a combination of 104 nickels and quarters totaling $22. Which system of linear equations can be used to find the num

Butoxors [25]

Answer:

The answer is c and we'll use c to get the actual answers.

A) n + q = 104

B) .05n + .25q = 22 we'll multiply B) by -4

B) -.2n -1q = -88 then we add A)

A) n + q = 104 which equals

.8n = 16

n = 20 nickels

q = 84 quarters

20 nickels = $1

84 quarters = $21

Successful!!!

Step-by-step explanation:

5 0

3 years ago

Milton purchase a 5 gallon aquarium for his bedroom.to fill the aquarium for his room. To fill the aquarium with water he uses a

svetlana [45]

There a 4 quarts in 1 gallon, so he will fill and empty the container 20 times.

6 0

3 years ago

HELPPP I SUCK AT MATH

e-lub [12.9K]

I think the answer is 6

4 0

3 years ago

The question in the image! Please hurry :D

sergey [27]

Answer:

While slavery was the major issue separating the North and South, it was not slavery itself that sparked the conflict. The South wanted to secede from the Union, and the North refused. While President Abraham Lincoln personally opposed slavery, he recognized that it was legal under the U.S. Constitution at the time. He also recognized that few in the North were ready to go to war to free the slaves. For Lincoln and the northern majority, preservation of the Union was the foremost goal.

6 0

2 years ago

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