PLEASE HELP IM IN A HURRY

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

Phantasy [73]

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:

$y=-2.95836 x +234.56159$

7 0

2 years ago

To better understand how husbands and wives feel about their finances, Money Magazine conducted a national poll of 1010 married

Xelga [282]

Answer:

a. See the table below

b. See the table below

c. 0.548

d. 0.576

e. 0.534

f) i) 0.201, ii) 0.208

Explanation:

First, order the information provided:

Table: "Who is better at getting deals?"

Who Is Better?

Respondent I Am My Spouse We Are Equal

Husband 278 127 102

Wife 290 111 102

a. Develop a joint probability table and use it to answer the following questions. 

The joint probability table shows the same information but as proportions. Hence, you must divide each number of the table by the total number of people in the set of responses.

1. Number of responses: 278 + 127 + 102 + 290 + 111 + 102 = 1,010.

2. Calculate each proportion:

278/1,010 = 0.275
127/1,010 = 0.126
102/1,010 = 0.101
290/1,010 = 0.287
111/1,010 = 0.110
102/1,010 = 0.101

3. Construct the table with those numbers:

Joint probability table:

Respondent I Am My Spouse We Are Equal

Husband 0.275 0.126 0.101

Wife 0.287 0.110 0.101

Look what that table means: it tells that the joint probability of being a husband and responding "I am" is 0.275. And so for every cell: every cell shows the joint probability of a particular gender with a particular response.

Hence, that is why that is the joint probability table.

b. Construct the marginal probabilities for Who Is Better (I Am, My Spouse, We Are Equal). Comment.

The marginal probabilities are calculated for each for each row and each column of the table. They are shown at the margins, that is why they are called marginal probabilities.

For the colum "I am" it is: 0.275 + 0.287 = 0.562

Do the same for the other two colums.

For the row "Husband" it is 0.275 + 0.126 + 0.101 = 0.502. Do the same for the row "Wife".

Table Marginal probabilities:

Respondent I Am My Spouse We Are Equal Total

Husband 0.275 0.126 0.101 0.502

Wife 0.287 0.110 0.101 0.498

Total 0.562 0.236 0.202 1.000

Note that when you add the marginal probabilities of the each total, either for the colums or for the rows, you get 1. Which is always true for the marginal probabilities.

c. Given that the respondent is a husband, what is the probability that he feels he is better at getting deals than his wife? 

For this you use conditional probability.

You want to determine the probability of the response be " I am" given that the respondent is a "Husband".

Using conditional probability:

P ( "I am" / "Husband") = P ("I am" ∩ "Husband) / P("Husband")

P ("I am" ∩ "Husband) = 0.275 (from the intersection of the column "I am" and the row "Husband)

P("Husband") = 0.502 (from the total of the row "Husband")

P ("I am" ∩ "Husband) / P("Husband") = 0.275 / 0.502 = 0.548

d. Given that the respondent is a wife, what is the probability that she feels she is better at getting deals than her husband?

You want to determine the probability of the response being "I am" given that the respondent is a "Wife", for which you use again the formula for conditional probability:

P ("I am" / "Wife") = P ("I am" ∩ "Wife") / P ("Wife")

P ("I am" / "Wife") = 0.287 / 0.498

P ("I am" / "Wife") = 0.576

e. Given a response "My spouse," is better at getting deals, what is the probability that the response came from a husband?

You want to determine: P ("Husband" / "My spouse")

Using the formula of conditional probability:

P("Husband" / "My spouse") = P("Husband" ∩ "My spouse")/P("My spouse")

P("Husband" / "My spouse") = 0.126/0.236

P("Husband" / "My spouse") = 0.534

f. Given a response "We are equal" what is the probability that the response came from a husband? What is the probability that the response came from a wife?

What is the probability that the response came from a husband?

P("Husband" / "We are equal") = P("Husband" ∩ "We are equal" / P ("We are equal")

P("Husband" / "We are equal") = 0.101 / 0.502 = 0.201

What is the probability that the response came from a wife:

P("Wife") / "We are equal") = P("Wife" ∩ "We are equal") / P("We are equal")

P("Wife") / "We are equal") = 0.101 / 0.498 = 0.208

6 0

3 years ago

$350, 6.2%, 3 years plzz help

KIM [24]

Answer:

not much info

Step-by-step explanation:

8 0

3 years ago

List 3 goods or services you have used that are funded by taxes

Tanzania [10]

Education school,Our military defense and Law enforcement like the Police.

5 0

3 years ago

Read 2 more answers

Solve the integral: <img src="https://tex.z-dn.net/?f=%20%5Cint%20%5C%3A%20%20%7Be%7D%5E%7B%20-%20%20%7Bx%7D%5E%7B2%7D%20%7D%

Sever21 [200]

$e^{-x^2}$ has no antiderivative in terms of elementary functions (polynomials, exponentials, logarithms, trigonometric functions, etc), but there is a special function defined to fit that role called the error function, $\mathrm{erf}(x)$ , where

$\mathrm{erf}(x)=\displaystyle\frac2{\sqrt\pi}\int_0^xe^{-t^2}\,\mathrm dt$

By the fundamental theorem of calculus, we can see that

$\dfrac{\mathrm d}{\mathrm dx}\mathrm{erf}(x)=\dfrac2{\sqrt\pi}e^{-x^2}$

which means we have

$\displaystyle\int e^{-x^2}\,\mathrm dx=\dfrac{\sqrt\pi}2\mathrm{erf}(x)+C$

8 0

3 years ago