Respuesta :
Answer:
The function for the model that gives the pressure in atm is given as:
P = 1.000 + 0.030*D
Step-by-step explanation:
From the question, we are given the Depth with corresponding P. Our duty is to calculate the Pressure (P) in the atm given the Depth (D). From this, we know that:
1. Pressure (P) is the dependent variable, and
2. Depth (D) is the independent variable.
Hence the function is a linear relationship which is known as regression equation. This can be achieve by estimating the:
i) Slope (β), and
ii) Intercept (α).
We can obtain the slope by:
[tex]\beta = \frac{n\sum(P)\sum(D) - \sum{PD}}{n\sum{D}^2 - (\sum{D})^2}[/tex], and
[tex]\alpha = \frac{\sum{P}}{n} - \beta \frac{\sum{D}}{n}[/tex].
Hence, the function is:
[tex]\hat{P}[/tex] = α + β D
You can achieve the task through R programming. Here is the R code.
#... this code in R programming
D = c(0,33,66,99,132)
P = c(1,2,3,4,5)
mod = lm(P~D)
mod.
############################
And we obtained P = 1.000 + 0.030 D
The equation is P = 0.030 D + 1
Linear system
It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.
Given
Depth D (feet, ft) Pressure P (atm)
33 2
66 3
99 4
132 5
Write the function for the model that gives the pressure in atm, where d is depth in feet.
Let the pressure be P and the depth be D.
We know the equation of the line is given by P = mD + c
For slope m
[tex]\rm m = \dfrac{y_2 - y_1}{x_2 - x_1}\\\\m = \dfrac{3-2}{66-33}\\\\m = 0.030[/tex]
So the equation will be P = 0.030 D + c
For D = 33, P will be 2 then the value of c will be
2 = 0.030(33) + c
c = 2 - 1
c = 1
Then the equation is P = 0.030 D + 1.
More about the linear system link is given below.
https://brainly.com/question/20379472
