Question

Consider the following table.

Answer 1

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:

$\beta = \frac{n\sum(P)\sum(D) - \sum{PD}}{n\sum{D}^2 - (\sum{D})^2}$, and

$\alpha = \frac{\sum{P}}{n} - \beta \frac{\sum{D}}{n}$.

Hence, the function is:

$\hat{P}$ = 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