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
Kamila [148]
3 years ago
14

Some types of algae have the potential to cause damage to river ecosystems. Suppose the accompanying data on algae colony densit

y (y) and rock surface area (x) for nine rivers is a subset of data that appeared in a scatterplot in a research paper in a scientific journal. Col1 x 50 55 50 79 44 37 70 45 49 Col2 y 152 48 22 35 43 171 13 185 25 (a) Compute the equation of the least-squares regression line. (Round your numerical values to five decimal places.)
Mathematics
1 answer:
Phantasy [73]3 years ago
7 0

Answer:

y=-2.95836 x +234.56159

Step-by-step explanation:

We assume that th data is this one:

x: 50, 55, 50, 79, 44, 37, 70, 45, 49

y: 152, 48, 22, 35, 43, 171, 13, 185, 25

a) Compute the equation of the least-squares regression line. (Round your numerical values to five decimal places.)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}

So we can find the sums like this:

\sum_{i=1}^n x_i =50+ 55+ 50+ 79+ 44+ 37+ 70+ 45+ 49=479

\sum_{i=1}^n y_i =152+ 48+ 22+ 35+ 43+ 171+ 13+ 185+ 25=694

\sum_{i=1}^n x^2_i =50^2 + 55^2 + 50^2 + 79^2 + 44^2 + 37^2 + 70^2 + 45^2 + 49^2=26897

\sum_{i=1}^n y^2_i =152^2 + 48^2 + 22^2 + 35^2 + 43^2 + 171^2 + 13^2 + 185^2 + 25^2=93226

\sum_{i=1}^n x_i y_i =50*152+ 55*48+ 50*22+ 79*35+ 44*43+ 37*171+ 70*13+ 45*185+ 49*25=32784

With these we can find the sums:

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=26897-\frac{479^2}{9}=1403.556

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=32784-\frac{479*694}{9}=-4152.22

And the slope would be:

m=-\frac{-4152.222}{1403.556}=-2.95836

Nowe we can find the means for x and y like this:

\bar x= \frac{\sum x_i}{n}=\frac{479}{9}=53.222

\bar y= \frac{\sum y_i}{n}=\frac{694}{9}=77.111

And we can find the intercept using this:

b=\bar y -m \bar x=77.1111111-(-2.95836*53.22222222)=234.56159

So the line would be given by:

y=-2.95836 x +234.56159

You might be interested in
Minimize Q=3x2+3y2​, where x+y=6.
weeeeeb [17]

Answer:

+(x + y) {}^{2}  = 6 {}^{2} \\ x {}^{2} + 2xy + y {?}^{2}  = 36

x {}^{2}  + y {}^{2}  = 36 - 2xy

q = 3(x {}^{2}  + y {}^{2} )

q = 3(36 - 2xy) = 108 - 6xy

5 0
2 years ago
What are the roots of the graph below?
Nostrana [21]

Answer:

-2,-1,1,2

Step-by-step explanation:

The term root is just another name for the x intercept so just look at where your line crosses the x axis and you will have your answer. Remember the y axis is not involved so it cannot be a co-ordinate.

4 0
3 years ago
Ms. Alba is on a business trip. Her company gave her $20 for 6 meals. She has spent $95 and has eaten 5 meals. Find x, the amoun
ipn [44]

Answer:

A

Step-by-step explanation:

4 0
2 years ago
.
strojnjashka [21]

For this case we have the variable x = -3:

A) 6x = 6 (-3) = - 18\\B) 4x = 4 (-3) = - 12\\C) -3x = -3 (-3) = + 9\\D) -7x = -7 (-3) = + 21

Now, matching each expression with its value we have:

A goes with 4

B goes with 3

C goes with 2

D goes with 1

ANswer:

A goes with 4

B goes with 3

C goes with 2

D goes with 1

6 0
3 years ago
What does W equal? <br> -22-3w-5w=0
DerKrebs [107]

In the International System of Units (SI), the unit of power is the watt (W), which is equal to one joule per second.

SI unit: watt (W)

In SI base units: kg⋅m2⋅s−3

3 0
3 years ago
Other questions:
  • On a blueprint, a square with 20 meters per side was shown as a square with 12 centimeters per side. how long would a girder app
    6·1 answer
  • Trigonometric problems.<br><br> Could someone help me with this? I’m confused.
    13·1 answer
  • Find the value of the d. 2d -5 = 17
    14·1 answer
  • Use a double integral to find the volume of the solid in the first octant bounded by the plane determined by the three non-colin
    15·1 answer
  • Does anyone know the answer to these questions???
    12·2 answers
  • What is one of the values for "X" that satisfy the equation x^2 - 7x - 18 ? A.-9 B. no solutions C.9 D.2​
    13·2 answers
  • What's 5sqrtx -4 = 20
    10·1 answer
  • Classify the triangle by its side lengths and by its angle measurements.
    11·1 answer
  • Is
    5·1 answer
  • Find the lowest common denominator (LCD) of<br> these fractions.<br> 2<br> 12<br> 3y
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!