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

Alex Ar [27]

Answer:

$y=-2.86 x +228.84$

Step-by-step explanation:

We assume that the data is this one:

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

y: 152, 53, 22, 35, 38, 166, 13, 185, 25

Find the least-squares line appropriate for this data.

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:

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

$\sum_{i=1}^n y_i =152 + 53 + 22 + 35 + 38 + 166 + 13 + 185 + 25=689$

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

$\sum_{i=1}^n y^2_i =152^2 + 53^2 + 22^2 + 35^2 + 38^2 + 166^2 + 13^2 + 185^2 + 25^2=91641$

$\sum_{i=1}^n x_i y_i =50*152+ 55*53+ 50*22+ 79*35+ 44*38+ 37*166 +70*13+ 45*185+ 49*25=32654$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=26897-\frac{479^2}{9}=1403.56$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=32654-\frac{479*689}{9}=-4016.11$

And the slope would be:

$m=-\frac{4016.11}{1403.56}=-2.86$

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

$\bar x= \frac{\sum x_i}{n}=\frac{479}{9}=53.22$

$\bar y= \frac{\sum y_i}{n}=\frac{689}{9}=76.56$

And we can find the intercept using this:

$b=\bar y -m \bar x=76.56-(-2.86*53.22)=228.84$

So the line would be given by:

$y=-2.86 x +228.84$

8 0

3 years ago

The heights (in inches) of the starting players on a high school basketball team are as follows: 72, 75, 78, 72, 73.

MakcuM [25]

Answer:

There are 5 starting players.

The mean is 74

The median is 73

Step-by-step explanation:

6 0

2 years ago

WHICH ONE IS IT!!!!!!!

Westkost [7]

ANSWER IS CCCCCCCCCCCCCCCCCCCCCCCCCC

4 0

3 years ago

Read 2 more answers

Can i plz get some help with this!<br>its about finding the conjecture<br>

Studentka2010 [4]

Answer:

3-they are cubes of consecutive natural numbers

1 cube is 1

2 cube is 8

3 cube is 27

and so on...

let me know if you're asking fourth one or third one

6 0

2 years ago

Match the vocabulary words with the right definitions. 1. a relation where for any given input value there is only one output va

pochemuha

Answer:

Step-by-step explanation:

1. Relation - a set of ordered pairs

2. Vertical line test - a test used to determine if a graph is a function; states that a vertical line can only go through one point on the graph to be a function

3. Function - a relation in which for any given input value, there is only one output value

4. Output - value generated by a function when an input value is substituted into the function and evaluated

5. Ordered pair - a group of two numbers written in the form (x, y) where the x value represents a horizontal position and the y value represents a vertical position

6. Mapping Diagram - a table or diagram that represents a mathematical relation

7. Input - a value that is substituted in for the variable in a function in order to generate an output value

3 0

2 years ago