( 69 points + brain cuz why not xd )
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A scatter diagram has points that show the relationship between two sets of data.
We have the following data,
where <em>x</em> is the average number of employees in a group health insurance plan and <em>y</em> is the average administrative cost as a percentage of claims.
To make a scatter diagram you must, draw a graph with the independent variable on the horizontal axis (<em>in this case x</em>) and the dependent variable on the vertical axis (<em>in this case y</em>). For each pair of data, put a dot or a symbol where the x-axis value intersects the y-axis value.
Linear regression is a way to describe a relationship between two variables through an equation of a straight line, called line of best fit, that most closely models this relationship.
To find the line of best fit for the points, follow these steps:
Step 1: Find and
as it was done in the below table.
Step 2: Find the sum of every column:
Step 3: Use the following equations to find intercept a and slope b:
Step 4: Assemble the equation of a line
Answer:
8.2 *10^5 ft lb
Step-by-step explanation:
Wcoal = 800*500 = 400000 = 4*10^5 ft lb
Using a right Riemann sum
The width of the entire region to be estimated = 400 - 0 = 400
Considering 8 equal subdivisions, then the width of each rectangular division is 400/8 = 50
F(x) = 6(400-y)
Wrope = 50(2100) + 50(1800) + 50(1500) + 50(1200) + 50(900) + 50(600)
+ 50(300) + 50(0) = 420000 = 4.2 * 10^5 ft lb
Note: Riemann sum is an approximation, so may not give a accurate value
work done = Wcoal + Wrope= 4*10^5+ 4.2 * 10^5 = 8.2 *10^5 ft lb