Scatter Diagrams

Question 10

Scatter diagrams between payment and other independent variables,

Chart one:

The scatter chart below represents the relationship between the number ofg rooms and the annual nursing salary:

The X axis represent the number of rooms while the Y axis is the annual nursing salary, from the scatter diagram we add a trend line and this hsows that as the number of rooms increase then the annual nursing salaryt also increases, therefore there is a psotive relationship between the two variables.

Chart two:

This chart representr the relationshhip between annula medial in patient days and annual nursing salary,:

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From this chart it is evident that there is a positive relationship between the tow variables, as the annual in patient days increase then the annual nursing salary also increases.

Chart three:

This chart shows the relationship between annual total patient days and annual nursing salary,

From the above chart it is evident that there is an inverse relationship between the two variables, as the annual total patient days increase then the annual nursing salary declines.

Chart four:

The chart shows the relationship between rural and non rural homes and the annual nursing salary:

From the above chart it is evident that rural homes will have a negative impact on the annual

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nursing salary, if the value of the dummy variable rural home is 1 then the annual nursing salary declines.

B.

the best variable to use would be the total in patients days, this is because we have to formulate a hypothesis that shows the number of in patient days and the salaries, this is due to the fact that we will assume that the more we attend to patients then the higher the number of working hours and therefore the higher the revenue and salaries.

C.

if two variables were to be chosen to estimate the annual nursing salary then the total in patient days and the rural and non home variable would be best to estimate salaries, this is because according to the variables we can formulate a hypothesis that the higher the annual in patient days then the higher the salaries and that rural homes will pay less than the non rural homes.

D.

Three variables that should be chosen include the annual number of in patient days, the rural and non rural variable and finally the number of beds.

E.

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highest r squared value:

Annual nursing salaries (\$100s)

r squared

Number of beds in home

0.591

Annual medical in-patient days (100s)

0.173

Annual total patient days (100s)

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0.021

Rural (1) and non-rural (0) homes

0.214

From the above results it is therefore evident that the number of beds in the home has the highest r squared value.

F.

Regression using independent variable x1(number of beds), x2(number of in patients days) and (the annual patient days) x3

We estimate the model:

Y = b0 + b1x1 + b2x2 +b3x3

b

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b0

1.206097

b1

0.531391

b2

-0.41411

b3

0.865304

Therefore our estimated model will be:

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Y = 1.206097 + 0.531391×1  -0.41411×2 + 0.865304×3

The above model means that if we hold all other factors constant and the value of all independent variables is zero then the annual nursing salary will be 1.206, if we hold all other factors constant and increase the number of beds in a home by one unit then the annual nursing slary will increase by 0.5313 units, if we hold all other factors constant and increase the annual number of inpatients by one unit then the annual nursing slary will decrease by 0.4141 units finally if we hold all other factors constant and increase the annual number of patients days by one unit then the annual nursing salary will increase by 0.8653 units.

Question 11

a.

Scatter diagram

From the scatter diagram the X axis is temperature while the y axis is the %o ring exxpansion, from the relationship it is evident that as the temperature icnreases the or ing exxpands.

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b.

We estimate the model y = b0 + b1 x where y is the % o ring expansion and x is the temperature,

b

b0

5.471042

b1

0.177769

From the above table we state our model as follows:

y = 5.471042 + 0.177769 x

from the result it is clear that the autonomous value is 5.471 and that an increase in temperature by one unit holding all other factors constant will result into an increase of 0.1777

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% o ring expansion.

c.

R squared

The r squared value is 0.966 which shows a very strong relationship between the two variables, this also means that 96.6% of variations in the dependent variable are explained by the independent variable.

d.

Launching a space shuttle at 29 degrees, the following will be the results:

y = 5.471042 + 0.177769 (29)

y = 10.62634

Therefore the expansion will be 10.62634%

e.

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From the question it is stated that the recommended expansion should be at least 5% for safe launch, therefore a 10% expansion resulting from 29 degrees would be okay and safe to launch.

Question 12

a.

Scatter diagram:

The scatter diagram below demonstrates the relationship between the PE ratio and returns, pe ratio is on the X axis while returns is on the y axis.

From the chart an increase in pe ratio will increase returns.

The chart below demonstrates the relationship between risk and returns,

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From the chart as risk increase then returns also increase.

b.

Estimating

Y = b0 + b1x1 +b2x2 where x1 is the peratio and x2 is risk while y is returns, the results of this is as follows:

b

b0

-0.00034

b1

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0.00013

b2

0.000183

Y = -0.00034+ 0.00013 x1 +0.000183 x2

From the model we have a negative autonomous value, from the model if we increase the pe ratio by one unit and hold all other factors constant then the returns will increase by 0.00013, if we hold all other factors constant and increase the risk by one unit then the returns will increase by 0.000183 units.

The r squared value is 0.663534

c.

Regression 2

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We estimate the model

Y = b0 + b1x1 +b2x2 + b3 x3 +b4 x4

The following table summarizes the results:

b

b0

-2.45797

b1

-1.18299

b2

-7.96862

b3

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-0.05875

b4

1.87753

Our estimated model will be

Y =-2.45797 -1.18299×1 -7.96862×2 -0.05875 x3 +1.87753 x4

The r squared value is 0.806485735

d.

The best model is the second model; this is because it has a greater r squared value meaning a stronger relationship between the dependent variable and the independent variable.

Question 19

a.

Scatter diagram

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The chart shows the relatiohsip between avergage performance and salry, the x axis being average performance and the y axis being the salary level.

The chart shows a positive relationship between the two variables

The chart below shows the relationship between salsry and years, the years are in the x axis while the salry level is on the y axis

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There is a positive relationship between fvasriables

The chart below shows the relatiohsip between certificates and salsry, the certificat variable I on the x axis while slary is ploted on the y axis.

There is a positive relationship between variables

b.

the best variable to use is the year variable, thios is because from the scatter diagram the stochastic values that deviate from the trned line are much less than the other variable.

c.

if we are to choose two variables then the bvest variables would be the yearsand the average performance variables.

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d.

variable name

r squared

1

years

0.737

2

average  performance

0.445

3

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certificate

0.311

The above table summarizes the r squared value for the salary variable and the other independent variables, from the table above it would be better to use the two variables in the estimation which include the years and average performance which have high r squared values.

e.

the following table summarizes the results:

b

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b0

0.87575

b1

0.028139

b2

0.00865

b3

0.03456

We state our model as follows:

Y = 0.87575 + 0.028139×1 + 0.00865×2 +0.03456×3

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f.

considering that we are given the number of years as 12, average performance as 4.5 and certificates as four then we can determine the value of salary, from the estimated model when we substitute the independent variables the salary for such a case is 1.244, this is not at 1.5 standard error of the model, for this reason the model would not be appropriate in estimation of salaries.

References:

Bluman A. (2000) Elementary Statistics: A Step by Step Approach, McGraw Hill press, New York

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