1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
dsp73
3 years ago
11

Consider the given data. x 0 2 4 6 9 11 12 15 17 19 y 5 6 7 6 9 8 8 10 12 12 Use the least-squares regression to fit a straight

line to the given data. Along with the slope and intercept, compute the standard error of the estimate and the correlation coefficient. Repeat the problem, but regress x versus y—that is, switch the variables. Interpret your results. (Round the final answers to four decimal places.) Least-squares regression: y versus x B

Mathematics
1 answer:
levacccp [35]3 years ago
5 0

Answer:

See below

Step-by-step explanation:

By using the table 1 attached (See Table 1 attached)

We can perform all the calculations to express both, y as a function of x or x as a function of y.

Let's make first the line relating y as a function of x.

<u>y as a function of x </u>

<em>(y=response variable, x=explanatory variable) </em>

\bf y=m_{yx}x+b_{yx}

where

\bf m_{yx} is the slope of the line

\bf b_{yx} is the y-intercept

In this case we use these formulas:

\bf m_{yx}=\frac{(\sum y)(\sum x)^2-(\sum x)(\sum xy)}{n\sum x^2-(\sum x)^2}

\bf b_{yx}=\frac{n\sum xy-(\sum x)(\sum y)}{n(\sum x^2)-(\sum x)^2}

n = 10 is the number of observations taken (pairs x,y)

<u>Note:</u> <em>Be careful not to confuse  </em>

\bf \sum x^2 with \bf (\sum x)^2

Performing our calculations we get:

\bf m_{yx}=\frac{(83)(95)^2-(95)(923)}{10*1277-(95)^2}=176.6061

\bf b_{yx}=\frac{10*923-(95)(83)}{10(1277)-(95)^2}=0.3591

So the equation of the line that relates y as a function of x is

<h3>y = 176.6061x + 0.3591 </h3>

In order to compute the standard error \bf S_{yx}, we must use Table 2 (See Table 2 attached) and use the definition

\bf s_{yx}=\sqrt{\frac{(y-y_{est})^2}{n}}

and we have that standard error when y is a function of x is

\bf s_{yx}=\sqrt{\frac{39515985}{10}}=1987.8628

Now, to find the line that relates x as a function of y, we simply switch the roles of x and y in the formulas.  

So now we have:

x as a function of y

(x=response variable, y=explanatory variable)

\bf x=m_{xy}y+b_{xy}

where

\bf m_{xy} is the slope of the line

\bf b_{xy} is the x-intercept

In this case we use these formulas:

\bf m_{xy}=\frac{(\sum x)(\sum y)^2-(\sum y)(\sum xy)}{n\sum y^2-(\sum y)^2}

\bf b_{xy}=\frac{n\sum xy-(\sum x)(\sum y)}{n(\sum y^2)-(\sum y)^2}

n = 10 is the number of observations taken (pairs x,y)

<u>Note:</u> <em>Be careful not to confuse  </em>

\bf \sum y^2 with \bf (\sum y)^2

Remark:<em> </em><em>If you wanted to draw this line in the classical style (the independent variable on the horizontal axis), you would have to swap the axis X and Y) </em>

Computing our values, we get

\bf m_{xy}=\frac{(95)(83)^2-(83)(923)}{10*743-(83)^2}=1068.1072

\bf b_{xy}=\frac{10*923-(95)(83)}{10(743)-(83)^2}=2.4861

and the line that relates x as a function of y is

<h3>x = 1068.1072y + 2.4861 </h3>

To find the standard error \bf S_{xy} we use Table 3 (See Table 3 attached) and the formula

\bf s_{xy}=\sqrt{\frac{(x-x_{est})^2}{n}}

and we have that standard error when y is a function of x is

\bf s_{xy}=\sqrt{\frac{846507757}{10}}=9200.5856

<em>In both cases the correlation coefficient r is the same and it can be computed with the formula: </em>

\bf r=\frac{\sum xy}{\sqrt{(\sum x^2)(\sum y^2)}}

Remark: <em>This formula for r is only true if we assume the correlation is linear. The formula does not hold for other kind of correlations like parabolic, exponential,..., etc. </em>

Computing the correlation coefficient :

\bf r=\frac{923}{\sqrt{(1277)(743)}}=0.9478

You might be interested in
What is the equation of the parabola?
irina1246 [14]

Because the parabola opens down and the vertex is at (0, 5), we conclude that the correct option is:

y  = -(1/8)*x² + 5.

<h3>Which is the equation of the parabola?</h3>

The relevant information is that we have the vertex at (0, 5), and that the parabola opens downwards.

Remember that the parabola only opens downwards if the leading coefficient is negative. Then we can discard the two middle options.

Now, because the parabola has the point (0, 5), we know that when we evaluate the parabola in x = 0, we should get y = 5.

Then the constant term must be 5.

So the correct option is the first one:

y  = -(1/8)*x² + 5.

If you want to learn more about parabolas:

brainly.com/question/4061870

#SPJ1

3 0
1 year ago
Please help, I need good grades in order to stay alive
astra-53 [7]

Answer:

help with what and same i need good grades or ima be dead

Step-by-step explanation:

XD

7 0
2 years ago
Find the volume of a cylinder if the radius is 12 inches and the height is 17 inches
Alex Ar [27]

Answer:

Volume of the cylinder = 7686.72\,inches^3

Step-by-step explanation:

Radius(r) of the cylinder= 12\,inches

Height(h) of the cylinder= 17\,inches

Volume of a cylinder is :

                   \pi \times r^2\times h

As,

          \pi =\dfrac{22}{7}=3.14

Volume is:  

            =3.14\times (12\times 12)\times 17\\\\=3.14\times 144 \times 17\\\\=3.14\times 2448\\\\=7686.72\,inches^3

The volume of the cylinder is: 7686.72\,inches^3                    

3 0
3 years ago
Find the surface area of the prism.
DanielleElmas [232]

Answer:

2 x 5 = 10, 10 x 2 = 20

4 x 2 = 8, 8 x 2 = 16

5 x 4 = 20, 20 x 2 = 40

40 + 20 + 16 = 76 yd^2 is your answer.

5 0
2 years ago
Read 2 more answers
Multiply 1/2x5/8 simplest form
lana [24]
1/2 x 5/8 = 5/16 in simplest form
3 0
3 years ago
Other questions:
  • If x+9.8=14.7, what is the value of 8(x-3.7?
    9·1 answer
  • The height, h, in feet of a golf ball above the ground after being hit into the air is given by the equation, h = -16t 2 + 64t,
    12·1 answer
  • A triangle with side lengths of 3, 4, and 5 forms a right triangle.<br><br> True<br> False
    12·2 answers
  • Use Pythagorean theorem to find the missing length. (round to tenth if necessary) IS
    6·1 answer
  • Write an integer to represent each situation:<br> Jillian deposited $47 he received for his birthday
    15·2 answers
  • Find AB. Round to the nearest tenth if necessary.<br>​
    10·1 answer
  • Please help me with 1,2,3,show me how you get the answers and show me the steps for 1,2,3,please do not send me link write it ri
    5·1 answer
  • How much wrapping paper did he use ,in square inches
    7·1 answer
  • What? I don’t under stand
    9·2 answers
  • Someone plssssss help me!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!