CORRELATION
AND REGRESSION
1.
June
and Jun are partners in the Chemistry Lab.
Their assignment is to determine how much copper (CuSO4) will dissolve
in water at 10, 20, 30, 40, 50, 60, and 70 
C. These lab
results are shown below where y is the weight in grams of copper sulfate which
will dissolve in 100g of water at X C. Sketch a
scatter diagram. Find the equation of the least squares line and compute Se.
C. These lab
results are shown below where y is the weight in grams of copper sulfate which
will dissolve in 100g of water at X C. Sketch a
scatter diagram. Find the equation of the least squares line and compute Se.
X 10 20 30 40 50 60 70
Y 17 21 25 28 33 40 49
2.
The
number of workers on an assembly line varies due to the level of absenteeism on
any given day. In a random sample of
production output from several days of work the following data were obtained
where x = number of workers absent from
assembly line and y = number of defects coming off the line.
X 3 5 0 2 1 2 7
Y 16 20 9 12 10 13 25
A) Draw a
scatter diagram for the data.
B) Find 
and b. What is the equation of the least squares
line?
and b. What is the equation of the least squares
line?
C)
Graph the least squares line on your scatter diagram.
D)
Find the standard error of estimate Se.
E)
Find a 95% confidence interval for the number of defects when four workers are
absent.
3.
In
placing a weekly order for hotdogs the concessionaire at a large baseball
stadium needs to estimate the size of the crowd that will attend the game. Advanced ticket sales often give a good
indication of expected attendance at games.
Data from six previous weeks of games are shown below, where x =
advanced ticket sales (in thousands) and y = number of hotdogs purchased (in
thousands) at the game.
X 45 64 37 58 41 29
Y 32 46 25 44 32 18
A) Draw a
scatter diagram for the data.
B) Find and b. What is the equation of the least squares
line?
and b. What is the equation of the least squares
line?
C)
Graph the least squares line on your scatter diagram.
D)
Find the standard error of estimate Se.
E)
Find a 95% confidence interval for the number of hotdogs to be prepared when
advanced ticket sales are 55 thousand.
4. The
Central Office of a large manufacturing company manager ten similar plants in
different locations. The following data
were obtained where x = percent of operating capacity being used at the plant
and y = profits in hundreds of thousands of dollars at the same plant.
X 50 61 77 80 82 85 88 81 95 99
Y 24 26 35 31 35 34 39 40 38 42
A) Draw a
scatter diagram for the data.
B) Find and b. What is the equation of the least squares
line?
and b. What is the equation of the least squares
line?
C)
Graph the least squares line on your scatter diagram.
D)
Find the standard error of estimate Se.
E)
Find a 95% confidence interval for the range of profits of a plant working at
75 percent capacity.
5. As director of personnel for a prosperous
company you have just hired a new public relations person. The final salary arrangements are negotiated
depending on the number of years of experience the new public relations person
brings to the company. After checking
with several other companies in your area you obtain the following data where x
= number of years of experience for a person in public relations and y = annual
salary in thousands of dollars.
X 1 2 15 11 9 6
Y 25 29 53 49 37 34
A) Draw a
scatter diagram for the data.
B) Find and b. What is the equation of the least squares
line?
and b. What is the equation of the least squares
line?
C)
Graph the least squares line on your scatter diagram.
D)
Find the standard error of estimate Se.
E)
Estimate a salary range for the candidate so that approximately 95% of the
public relations officers with 8 years of experience will be in this range.
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