1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
strojnjashka [21]
3 years ago
5

Let x be the average number of employees in a group health insurance plan, and let y be the average administrative cost as a per

centage of claims.
x 3 7 15 32 74
y 40 35 30 25 17

a) Make a scatter diagram of the data and visualize the line you think best fits the data.

Mathematics
1 answer:
Step2247 [10]3 years ago
6 0

A scatter diagram has points that show the relationship between two sets of data.

We have the following data,

\left\begin{array}{ccccccc}\mathrm{x}&3&7&15&32&74\\\mathrm{y}&40&35&30&25&17\end{array}\right

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 X\cdot Y and X\cdot X as it was done in the below table.

Step 2: Find the sum of every column:

\sum{X} = 131 ~,~ \sum{Y} = 147 ~,~ \sum{X \cdot Y} = 2873 ~,~ \sum{X^2} = 6783

Step 3: Use the following equations to find intercept a and slope b:

\begin{aligned}        a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} =             \frac{ 147 \cdot 6783 - 131 \cdot 2873}{ 5 \cdot 6783 - 131^2} \approx 37.05 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2}        = \frac{ 5 \cdot 2873 - 131 \cdot 147 }{ 5 \cdot 6783 - \left( 131 \right)^2} \approx -0.292\end{aligned}

Step 4: Assemble the equation of a line

\begin{aligned} y~&=~a ~+~ b \cdot x \\y~&=~37.05 ~-~ 0.292 \cdot x\end{aligned}

You might be interested in
I need help on this question ASAP
Kipish [7]
R>-6
Please correct me if I’m wrong
7 0
3 years ago
Show work on 8x+3y=-9
kozerog [31]
Work on 8x + 3y =-9.
6 0
3 years ago
What is the difference between 3/7 and 1/14 ?
mars1129 [50]

It would be: 3/7-1/14 = 6-1 / 14 = 5/14

So, 5/14 is your answer..........

8 0
3 years ago
The value of the digit 8 in this number is 8
Nana76 [90]
And... i don't get it

6 0
3 years ago
When was pi discovered
Murljashka [212]

Pi was discovered way back already the way to Babylonians and Egyptians 216 BC but none were all the way accurate they were close

8 0
3 years ago
Read 2 more answers
Other questions:
  • Ron started a new job which paid him $60 for the first day of training. after the first day, he will be paid $7 per hour. write
    11·2 answers
  • THIS IS HARD FOR M I NEED HELP!!!!!
    8·2 answers
  • Can someone help me with 3 4 and 5?? WILL MARK BRAINLIEST!! PLZZ helpppp meee :(((
    6·2 answers
  • Multiply (−7)(2)(−2).
    15·2 answers
  • 16.5−13.45+7.293 equals
    12·2 answers
  • Im giving brainlyest to first CORECT answer and 30points QUICKKKKKK
    8·1 answer
  • Quadrilateral IJKL is similar to quadrilateral MNOP. Find the measure of side NO. Round your answer to the nearest tenth.
    14·2 answers
  • Your school wants to test the fire alarm system during the two hour period between 9:00 a.M. And 11:00 a.M. The probability of t
    8·1 answer
  • Given that the measure of angle 3 is 75o. What is the value of x if the measure of angle 7 is (x + 40) ?
    10·2 answers
  • Solve each equation. Round to the nearest ten-thousandth. Check your answers.<br> 25²x⁺¹=144
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!