nissan stocks - data analysis

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Julie Boulos Buzzelli MPM4U1-02 December 2013

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Page 1: Nissan Stocks - Data Analysis

Julie Boulos

Buzzelli

MPM4U1-02

December 2013

Page 2: Nissan Stocks - Data Analysis

2

Nissan: Table of Contents

Part A: Business Description ………………………………………………….…..….Page 4

Part B: Mathematical Analysis of Collected Data

Line of Best Fit……………………………………………..………………………...…Page 6

Linear Regression…………………………………………………….………..…….Pages 7-9

Measures of Central Tendencies………………………………………...…………....Page 10

Standard Deviation……………………………………………………..……………...Page 10

Co-relation coefficient……………………………………………….…...…...…….….Page 11

Probability Distribution Formation………………………………………….……….Page 12

Box and Whisker Plot………………………………………………………...…...Pages 12-14

Part C: Written Paper on Mathematical Analysis with graphs

2008…………………………………………..…………………………………...Pages 16-19

2009………………………………………………………………………….……Pages 20-23

2010………………………………………………………………………...……..Pages 24-27

2011………………………………………………………………….…...……….Pages 28-31

2012………………………………………………………………….…............…Pages 32-35

2008-2012…………………………………………………………….…………...Pages 36-39

Part D: Written Report on Mathematical Understanding of material....................Page 41

Part E: Appendices, Rough Work, Miscellaneous and Bibliography…….……….Page 43

Page 3: Nissan Stocks - Data Analysis

3

PART A: BUSINESS DESCRIPTION

Page 4: Nissan Stocks - Data Analysis

4

“The power comes from inside.” This simple phrase familiar to every Nissan employee

conveys a powerful truth. Any company is only as strong as the people who bring it to life.

Companies do not create products, deliver services or solve problems; people do. The people

working at Nissan are facing major evolutions that are changing the global automotive industry

as we know it today.

The world's population is expanding at a rapid pace, from 6.7 billion today to more than

9 billion by 2050. More people will create the demand for more cars. Today, there are 600

million vehicles worldwide; by 2050, statistics show there may be up to 2.5 billion vehicles. A

car is an important symbol of freedom, status and personal achievement, and growing numbers

of new drivers will seek affordable transportation and the benefits that car ownership provides.

Another important trend is the growing demand for a cleaner environment. Automakers

are accelerating the development of products to offer greater fuel efficiency and fewer

CO2 emissions, from more efficient gasoline-fuelled engines to hybrids, clean diesel,

electric vehicles and fuel cell vehicles.

The world is changing, and Nissan is adapting with it. They are harnessing the power that's

inside Nissan to prepare solutions that our customers will want and value, now and in the years

to come. Solutions such as:

electric and fuel cell vehicles that are attractive, fun-to-drive cars with the appealing benefit

of zero emissions;

global entry cars that make mobility more accessible and affordable for all; and

innovative technological advances that are good for the environment, enhance safety,

improve dynamic performance or provide greater life-on-board satisfaction.

Nissan has a clear vision for the future, and - with their Alliance partner, Renault - they are

working with passion to achieve it. Their mission is to enrich people's lives, building trust with

their employees, customers, dealers, partners,

shareholders and the world at large.

Page 5: Nissan Stocks - Data Analysis

5

PART B: MATHEMATICAL

ANALYSIS OF COLLECTED DATA

Page 6: Nissan Stocks - Data Analysis

6

Line of Best Fit

Line of Best Fit (LOBF): the straight line that passes closest to the majority of the data points

on a scatter plot and best represents the relationship between two variables. The data is used to

form a curve of best fit. The stronger the correlation, the more closely the points cluster the

LOBF.

Formula used: y = ax + b, where the slope is represented by a, the y-intercept in represented by

b, and the individual point of the line is (x,y),

Slope = ∑ ∑ ∑

∑ ∑

Y-intercept = ̅ ̅

Let x represent the day # and y represent the open value.

In order to calculate the numerator, the total number of terms is multiplied by the sum of

Day*Open (∑ ), then yousubtract the product of the sum of Day (x)multiplied by the sum of

Open (y) from the first value (total number of terms by sum of day times open).

To calculate the denominator, the total number of terms is multiplied by the sum of Day^2

(∑ , followed by subtracting the sum of Day [∑ .

The numerator is then divided by the denominator, resulting in the slope.

Next, plug in your numbers and calculate the y-intercept, b = ̅ ̅.

To calculate the ̅ (mean of x) in the y-intercept equation, the sum of Day (∑ is divided by

the number of terms, the ̅ (mean of y) is similar except sum of Open (∑ rather than day.

After plugging in all the terms you can solve for the y-intercept

The LOBF is then determined by substituting the slope (a value), and y-intercept (b value) into

the equation

if using Microsoft Excel, calculate the numerator and denominator seperately so you can use

them to easily calculate the slope

A scatter plot is used to depict the line of best accurately

Page 7: Nissan Stocks - Data Analysis

7

Linear Regression

Linear Regression: an analytical technique used to determine the relationship between a

dependent and independent variable.

When the two variables have a linear correlation, you can develop a model of a relationship

between the x and y variables by finding a line of best fit.

In order to extrapolate, the estimated day (x) is substituted in the equation y = ax+b for the

LOBF to solve for the open value (y).

For Example: in the Nissan stock, a year’s time period is 261 days and the five-year time period

is 1273 days. In order to extrapolate, it would be 1273 (the five years) and

as our independent

x value.

Estimating the stock one month into the future:

x = 1273 +

y = -0.005741814x + 19.87823496

y = -0.005741814(1273+21.75) + 19.87823496

y= -0.005741814(1294.75) + 19.87823496

y = -7.4342136765 + 19.87823496

y = 12.4440212835

Therefore, the estimated value of the stock one month into the future is $12.44. The

average stock value of the five years is $16.22. This means that investing in Nissan is not the

best idea because the stock value is expected to drop again meaning you would lose money.

Page 8: Nissan Stocks - Data Analysis

8

6 months:

In order to extrapolate, it would be 1273 (the five years) and

as our independent x value.

Estimating the stock six months into the future:

x = 1273 +

y = -0.005741814x + 19.87823496

y = -0.005741814(1273+130.5) + 19.87823496

y= -0.005741814(1403.5) + 19.87823496

y = - 8.058635949 + 19.87823496

y = 11.819599011

The stock will only continue to decrease after six months still resulting in a poor

investment.

1 year:

In order to extrapolate, it would be 1273 (the five years) and

as our independent x value.

Estimating the stock one year into the future:

x = 1273 +

y = -0.005741814x + 19.87823496

y = -0.005741814(1273+261) + 19.87823496

y= -0.005741814(1534) + 19.87823496

y = - 8.807942676 + 19.87823496

y = 11.070292284

As the year concludes, the stock is estimated to continue decreasing in value.

Page 9: Nissan Stocks - Data Analysis

9

10 years:

In order to extrapolate, it would be 1273 (the five years) and

as our independent x value.

Estimating the stock ten years into the future:

x = 1273 +

y = -0.005741814x + 19.87823496

y = -0.005741814(1273+2610) + 19.87823496

y= -0.005741814(3883) + 19.87823496

y = - 22.295463762 + 19.87823496

y = -2.417228802

After completing all the calculations, it is proven that by estimation, Nissan stocks are

estimated to continue to drop in value. By looking at the calulations, I have concluded that it is

possible that in 10 years the stock will lose its value and the company can become bankrupt.

Page 10: Nissan Stocks - Data Analysis

10

Measures of Central Tendancy

When looking at a set of data, there are measures that can be taken in order to analyze the

data recorded

The three measures of central tendancy include the mean, median and mode

These are most frequently used to analyze the “middle”

Mean: the average of any set of data, takes the form of ∑

. (16.22069969)

Median: a method to calculate the middle number, but the data must be in ascending or

descending order. The number that sits in the middle is the median. (17.15)

Mode: the value that occurs most often, in most scenarios this is rarely used. It is not used as

much as the other measures because it does not accurately represent all the values in a set of

data, rather only the accounts for a certain set value that occurs most frequently. (16.45)

Calculations: y = ax + b, where a = ∑ ∑ ∑

∑ ∑ and b = ̅ ̅

Standard Deviations

Standard Deviation : the square root of the mean of the squares of the deviations of a set of

data. It is represented by the greek letter sigma and shows how much variation exists from the

average. The more spread out the data, the higher the deviation.

Formula : √∑

Start by calculating the numerator, the sum of each open value minus the mean of the data

square-rooted, then the overall difference is squared. Once you’ve calculated your numerator

you can divide it by your total number of terms.

The second method for standard deviation is the computer generated equation. It can be

calculated on Microsoft Excel using the equation =STDEV(C:C), C represents the column with

the open stock values.

Page 11: Nissan Stocks - Data Analysis

11

Co-relation Coefficient

Correlation: a number between -1 and 1, calculated to represent the linear dependence of two

variables or sets of data.

The number shows the relation between two variables, it shows whether the increase/decrease of

one factor has an effect on the other and by how much.

If the correlation is positive, it is a positive relationship, vise versa for negative. The strength of

the correlation varies from weak to medium to perfect. As seen in the diagram below, each range

is categorized differently. If the number is very close to 0, however, it means that there is barely

or no relationship between the two variables.

The equation for the co-relation coefficient is as follows:

r = ∑ ∑ ∑

√[ ∑ ∑ [ ∑ ∑

where r represents the co-relation coefficient.

Positive Negative

-1 -0.67 -0.33 0 0.33 0.67 1

Perfect Strong Moderate Weak Weak Moderate Strong Perfect

Page 12: Nissan Stocks - Data Analysis

12

Probability Distribution Formation

Probability Distribution Formation: taking the entire set of data and distributing it into various

possible occuring events, this can be represented using a histogram.

Histogram: similar to a bar graph, which helps group data into intervals. It can describe the

likeliness of the various events. I.e. which area will most sets of data occur.

To determine the probability distribution in excel, the maximum and minimum value of

each year is required. Then you must create intervals for which the sets of data are grouped in.

For example, if the minimum value is 3.6 and the maximum is 7.4, you need to choose and

interval that includes all the data points. 3 and 8 can be used in this example, with intervals of .5.

You can then proceed to code the document so that your first interval is calculated, you can do

this by creating a loop. Then, use your loop to calculate the next one and subtract your previous

intervals results to eliminate repetition.

Box and Whisker Plot

The box and whisker plot is a diagram that summarizes a set of data by representing the

first quartile, the median and third quartile. This is done with a box and the lowest and highest

data value with the ends of lines extending from the box.

0 10 20 30 40 50

Q1 Median Q3

Page 13: Nissan Stocks - Data Analysis

13

Starbucks Open Value 2008: Box and Whisker Plot

Looking at the box and whisker plot, the median is closer to Q3 than Q1. This shows the

fluctuation in open stock values throughout the year. There was a larger overall decrease vs

increase of prices throughout the year.

Starbucks Open Value 2009: Box and Whisker Plot

Looking at the box and whisker plot, by a small value the median is closer to Q3 than Q1

again. This shows the fluctuation in open stock values throughout the year. There was a larger

overall decrease rather than increase of prices throughout the 2009 year.

Starbucks Open Value 2010: Box and Whisker Plot

Looking at the box and whisker plot, the median is much closer to Q1 than Q3. This

shows the fluctuation in open stock values throughout the year. There was a larger overall

increase than decrease of prices throughout the 2010 year. The company begins to improve their

stock profits.

Q1 Q3 Median

Q1 Q3

Median Q1 Q3

Median

Min. Max.

Min. Max.

Min. Max.

Page 14: Nissan Stocks - Data Analysis

14

Starbucks Open Value 2011: Box and Whisker Plot

Looking at the box and whisker plot, the median is closer to Q1 than Q3. This shows the

fluctuation in open stock values throughout the year. There was a greater overall increase than

decrease of prices throughout the 2011 year. The company continues to improving their stock

profits.

Starbucks Open Value 2012: Box and Whisker Plot

Looking at the box and whisker plot, by a small value the median is still closer to Q1 than

Q3. This shows the fluctuation in open stock values throughout the year. The overall increase

was greater than the decrease of prices throughout the 2012 year.

Starbucks Open Value 2008-2012: Box and Whisker Plot

Looking at the box and whisker plot, by a small value the median is closer to Q3 than Q1

again. This shows the fluctuation in open stock values throughout the five years. Over the time

period, there was an overall decrease in stock prices since the open values kept fluctuating but

mostly declined. Even with some good years for Nissan, they still had an overall decline.

Q1 Q3 Median

Q1 Q3 Median

Q1 Q3 Median

Min. Max.

Min. Max.

Min. Max.

Page 15: Nissan Stocks - Data Analysis

15

PART C: WRITTEN PAPER ON MATHEMATICAL

ANALYSIS WITH GRAPHS

Page 16: Nissan Stocks - Data Analysis

16

2008

Line of Best Fit

m = ∑ ∑ ∑

∑ ∑ b = ̅ ̅

m =

b = 14.74411067 – (0.050099)(127)

m = 0.050099274 b = 8.381

Line of best fit: y = 0.050x + 8.381

The line of best fit indicates that the approximate initial stock value was $8.38. The initial

stock value was low, but the stock has a positive slope as the price is increasing at a good pace.

The lowest price for this year is $6.60 and the highest is $21.48.

y = 0.0501x + 8.3815 R² = 0.8106

0

5

10

15

20

25

0 50 100 150 200 250 300

Op

en (

$)

Day (x)

NISSAN OPEN STOCK VALUE 2008

Open

Linear (Open)

Page 17: Nissan Stocks - Data Analysis

17

Standard Deviation

Calculations: = √∑

=

= 4.063989611

OR =STDEV(C3:C3000)

= 4.063989611

The standard deviation for the year 2008 indicates that Nissan’s open stock value

deviates a bit from the mean of the open stock values for the years, which was $7.16. The

deviation is also observed through the range ($), which indicates the overall fluctuation

throughout the year. Furthermore, the deviation of data in 2008 causes a larger gap to form

between the clusters of data which is represented by the fluctuation on the graph.

Co-relation Coefficient

Equation: r = ∑ ∑ ∑

√[ ∑ ∑ [ ∑ ∑

√[ [

= 0.900337514

The correlation coefficient of 2008 indicates that the data has a positive correlation,

which means as the stock progresses over the year, the open stock value will continue to

increase. The strength of this correlation is considered to be a strong positive linear

correlation.

Page 18: Nissan Stocks - Data Analysis

18

Measures of Central Tendency

Equation: ∑

=

Mean: $14.74411067

Median: $16.08

Mode: $18.36

Therefore, the average Open Stock Value for the year 2008 is $14.74. The middle

number is $16.08 and the most frequently occuring value is $18.36. Considering the most

frequent value is higher than the average and the middle number, the 2008 year can be

considered to have positive values.

Page 19: Nissan Stocks - Data Analysis

19

Probability Distribution Formation

In conclusion, looking at this histogram we are able to analyze the different ranges of

data for the open stock values. The stock prices range from $6-23.99 which gives a pretty wide

range for the year. Just at a quick glance it is easy to see that the most frequent stock values

range from $15-17.99. With such a wide range of stock values it shows that the open stock

values were inconsistent.

020406080

100120140

# o

f O

ccu

ren

ces

Range ($)

2008 Nissan Open Distribution

Page 20: Nissan Stocks - Data Analysis

20

2009

Line of Best Fit

m = ∑ ∑ ∑

∑ ∑ b = ̅ ̅

m =

b = 11.63206349– (-0.043) (126.5)

m = -0.04295518 b = 17.06

Line of best fit: y = -0.043x + 17.06

The line of best fit indicates that the approximate initial stock value was $17.06. The

initial stock value was much higher then the year end. The 2009 stocks have a negative slope

since the price is gradually decreasing. The lowest price for this year is $5.65.

y = -0.043x + 17.066 R² = 0.8921

0

5

10

15

20

0 50 100 150 200 250 300

Op

en (

$)

Day

NISSAN OPEN STOCK VALUES 2009

Open Linear (Open)

Page 21: Nissan Stocks - Data Analysis

21

Standard Deviations

Calculations: = √∑

=

= 3.308383127

OR =STDEV(C3:C3000)

= 3.308383127

The standard deviation for the year 2009 indicates that Nissan’s open stock value

deviates a bit from the mean of the open stock values for the years, which was $17.06.

The deviation is also observed through the range ($), which indicates the overall

fluctuation throughout the year. Furthermore, the deviation of data in 2009 causes a gap

to form between the clusters of data as seen above on the graph.

Co-relation Coefficient

Equation: r = ∑ ∑ ∑

√[ ∑ ∑ [ ∑ ∑

√[ [

= -0.94450933

The correlation coefficient of 2009 indicates that the data has a negative correlation,

which means as the stock progresses over the year, the open stock value will continue to

decrease. The strength of this correlation is considered to be a strong negative linear

correlation.

Page 22: Nissan Stocks - Data Analysis

22

Measures of Central Tendency

Equation: ∑

=

Mean: $11.63206349

Median: $12.255

Mode: $14.35

Therefore, the average Open Stock Value for the year 2009 is $11.63. The middle number is

$12.26 and the most frequently occuring value is $14.35. Considering the most frequent value is

lower than the average and the middle number, the 2009 year is proving to be a declining year.

Page 23: Nissan Stocks - Data Analysis

23

Probability Distribution Formation

In conclusion, looking at this histogram we are able to analyze the different ranges of

data for the open stock values. The stock prices range from $5-18.99 which doesn’t give as wide

a range as the previous year but still gives a wide range for the year. Just at a quick glance it is

easy to see that the most frequent stock values range from $13-14.99. With such range of stock

values, and more occurences in the lower values, it shows the gradual decrease in stock prices

throughout the year.

0

20

40

60

80

100

# o

f O

ccu

ren

ces

Intervals ($)

2009 Nissan Open Distributions

Page 24: Nissan Stocks - Data Analysis

24

2010

Line of Best Fit

m = ∑ ∑ ∑

∑ ∑ b = ̅ ̅

m =

b = 16.74150794– (-0.00829)(126.5)

m = -0.00829696 b = 17.79

Line of best fit: y = -0.008x + 17.79

The line of best fit indicates that the approximate initial stock value was $17.79. The

initial stock value was not much higher then the year end. The 2010 stocks have a weak negative

slope since the price is decreasing. The lowest price for this year is $14.30.

y = -0.0083x + 17.791 R² = 0.1958

0

5

10

15

20

25

0 50 100 150 200 250 300

Op

en (

$)

Day (x)

NISSAN OPEN STOCK VALUES 2010

Open

Linear (Open)

Page 25: Nissan Stocks - Data Analysis

25

Standard Deviations

Calculations: = √∑

=

= 1.36394361

OR =STDEV(C3:C3000)

= 1.36394361

The standard deviation for the year 2010 indicates that Nissan’s open stock value

deviates a bit from the mean of the open stock values for the years, which was $17.79.

The deviation is also observed through the range ($), which indicates the overall

fluctuation throughout the year. Furthermore, the deviation of data in 2010 causes a small

gap between the clusters of data which is represented by the line on the graph.

Co-relation Coefficient

Equation: r = ∑ ∑ ∑

√[ ∑ ∑ [ ∑ ∑

√[ [

= -0.44251615

The correlation coefficient of 2010 indicates that the data has a negative correlation,

which means as the stock progresses over the year, the open stock value will continue to

decrease. The strength of this correlation is considered to be a moderate negative linear

correlation.

Page 26: Nissan Stocks - Data Analysis

26

Measures of Central Tendency

Equation: ∑

=

Mean: $16.74150794

Median: $16.45

Mode: $16.45

Therefore, the average Open Stock Value for the year 2010 is $16.74. The middle

number is $16.45 and the most frequently occuring value is $16.45. For this years the numbers

are generally in a small range, the average, most frequent, and middle numbers are all similar, if

not the same which shows very little change throughout the year. This year had a slight decrease

and then stayed in a very small range for the rest of the year.

Page 27: Nissan Stocks - Data Analysis

27

Probability Distribution Formation

In conclusion, looking at this histogram we are able to analyze the different ranges of

data for the open stock values. The stock prices range from $13-20.99 which gives a pretty wide

range for the year. Just at a quick glance it is easy to see that the most frequent stock values

range from $16-16.99. Although there is a wide range of stock values the majority of open stock

values are within the $16-16.99 range, this shows how the correlation is moderate.

Mean: $14.74411067

Median: $16.08

Mode: $18.36

0

50

100

150

# o

f O

ccu

ren

ces

Intervals ($)

2010 Nissan Open Distributions

Page 28: Nissan Stocks - Data Analysis

28

2011

Line of Best Fit

m = ∑ ∑ ∑

∑ ∑ b = ̅ ̅

m =

b = 18.92870079 – (0.009)(127.5)

m = 0.009695182 b = 17.79

Line of best fit: y = -0.009x + 17.69

The line of best fit indicates that the approximate initial stock value was $17.69. The

initial stock value was lower then the year end of $19.40. The 2011 stocks have a weak positive

slope since the price is slowly beginning to increase. The lowest price for this year is $16.20 and

the highest was $21.94. Although it had slow increases and a few drops, 2011 did much better

than 2009 and 2010.

y = 0.0097x + 17.693 R² = 0.2319

0

5

10

15

20

25

0 50 100 150 200 250 300

Op

en (

$)

Day (x)

NISSAN OPEN STOCK VALUES 2011

Open

Linear (Open)

Page 29: Nissan Stocks - Data Analysis

29

Standard Deviations

Calculations: = √∑

=

= 1.476111981

OR =STDEV(C3:C3000)

= 1.476111981

The standard deviation for the year 2011 indicates that Nissan’s open stock value

deviates a bit from the mean of the open stock values for the years, which was $17.69. The

deviation is also observed through the range ($), which indicates the overall fluctuation

throughout the year. Furthermore, the deviation of data in 2011 does not have a large gap between

the clusters of data which is represented by the fluctuation on the graph.

Co-relation Coefficient

Equation: r = ∑ ∑ ∑

√[ ∑ ∑ [ ∑ ∑

√[ [

= 0.481588795

The correlation coefficient of 2011 indicates that the data has a positive correlation,

which means as the stock progresses over the year, the open stock value will continue to

increase. The strength of this correlation is considered to be a moderate positive linear

correlation.

Page 30: Nissan Stocks - Data Analysis

30

Measures of Central Tendency

Equation: ∑

=

Mean: $18.92870079

Median: $18.725

Mode: $17.5

Therefore, the average Open Stock Value for the year 2011 is $18.93. The middle number is

$18.72 and the most frequently occuring value is $17.50. After looking at the past two years, all

the values have increased which shows that the company is gradually doing better.

Page 31: Nissan Stocks - Data Analysis

31

Probability Distribution Formation

In conclusion, looking at this histogram we are able to analyze the different ranges of

data for the open stock values. The stock prices range from $16-21.99 which is not a wide range

for the year. Many different values occur frequently, but the most frequent open value is in the

$17-17.99 range. For the majority of the year there are not too many large increases or decreases,

this shows the company stablizing.

Mean: $14.74411067

Median: $16.08

Mode: $18.36

0

20

40

60

80

# o

f O

ccu

ren

ces

Intervals ($)

2011 Nissan Open Distribution

Page 32: Nissan Stocks - Data Analysis

32

2012

Line of Best Fit

m = ∑ ∑ ∑

∑ ∑ b = ̅ ̅

m =

b = 18.94421456 – (0.007)(131)

m = 0.007533049 b = 17.79

Line of best fit: y = 0.007x + 17.95

The line of best fit indicates that the approximate initial stock value was $17.79. The

2012 stocks have a weak positive slope since the price is slowly continuing to increase. The

lowest price for this year is $16.60 and the highest was $21.77. The closing price for the 2008-

2012 five-year span was $17.70.

y = 0.0075x + 17.957 R² = 0.2397

0

5

10

15

20

25

0 50 100 150 200 250 300

Op

en (

$)

Day (x)

NISSAN OPEN STOCK VALUES 2012

Open

Linear (Open)

Page 33: Nissan Stocks - Data Analysis

33

Standard Deviations

Calculations: = √∑

=

= 1.159305453

OR =STDEV(C3:C3000)

= 1.159305453

The standard deviation for the year 2012 indicates that Nissan’s open stock value

deviates a bit from the mean of the open stock values for the years, which was $17.79. The

deviation is also observed through the range ($), which indicates the overall fluctuation

throughout the year. Furthermore, the deviation of data in 2012 causes a gap to re-form between

the clusters of data which is represented by the fluctuation on the graph.

Co-relation Coefficient

Equation:r = ∑ ∑ ∑

√[ ∑ ∑ [ ∑ ∑

√[ [

= 0.489575394

The correlation coefficient of 2012 indicates that the data has a positive correlation,

which means as the stock progresses over the year, the open stock value will continue to

increase. The strength of this correlation is considered to be a moderate positive linear

correlation.

Page 34: Nissan Stocks - Data Analysis

34

Measures of Central Tendency

Equation: ∑

=

Mean: $18.94421456

Median: $18.89

Mode: $18.71

Therefore, the average Open Stock Value for the year 2012 is $18.94. The middle number is

$18.89 and the most frequently occuring value is $18.71. Similarly to 2011, 2012 also has

similar measures of central tendancy. As seen on the line of best fit, the majority of the numbers

stay within the same range.

Page 35: Nissan Stocks - Data Analysis

35

Probability Distribution Formation

In conclusion, looking at this histogram we are able to analyze the different ranges of

data for the open stock values. The stock prices range from $16-22.49 which gives a decent

variety for the range of the year. Just at a quick glance it is possible to see that the most frequent

stock values range from $18.50-19.49.

Mean: $14.74411067

Median: $16.08

Mode: $18.36

0

20

40

60

80

100

# o

f O

ccu

ren

ces

Intervals ($)

2012 Nissan Open Distribution

Page 36: Nissan Stocks - Data Analysis

36

2008 – 2012

Line of Best Fit

m = ∑ ∑ ∑

∑ ∑ b = ̅ ̅

m =

b = 16.22069969 – (-0.0057)(637)

m = -0.005741814 b = 19.90

Line of best fit: y = -0.005x + 19.90

The line of best fit indicates that the approximate initial stock value was $19.90. The

initial stock value was lower then the year end of $21.48. Overall at the end of the five-year span

the stock value has an ending increased value. Even though the value has increased there is a

negative slope. The lowest price over the five years was $5.65 and the highest was $21.94.

Although it had many increases and drops, the Nissan stock managed to come back up to an

acceptable value. Using the data we can see that their worst year was 2009 since the data was

inconsistent and dropped significantally, and their best year was 2011 as the value finally

increased after a two-year decline.

y = -0.0058x + 19.908 R² = 0.3188

0

5

10

15

20

25

0 500 1000 1500

Op

en (

$)

Day (x)

NISSAN OPEN STOCK VALUES 2008 - 2012

Open x

Linear (Open x)

Page 37: Nissan Stocks - Data Analysis

37

Standard Deviations

Calculations: = √∑

=

= 3.765369664

OR =STDEV(C3:C3000)

= 3.765369664

The standard deviation for the five years indicates that Nissan’s open stock value

deviates from the mean of the open stock values for the years, which was $7.16. The deviation is

also observed through the overall range of the five years ($), which indicates the overall

fluctuation throughout the time period. Furthermore, even with some slow years, the deviation of

data causes a large gap to form between the clusters of data which is represented by the

fluctuation on the graph.

Co-relation Coefficient

Equation: r = ∑ ∑ ∑

√[ ∑ ∑ [ ∑ ∑

√[ [

= -0.556553684

The correlation coefficient of the five years indicates that the data has a negative

correlation, which means as the stock progresses over the years, the open stock value will

continue to decrease. The strength of this correlation is considered to be a moderate negative

linear correlation. Even though the stock does have some positive years, the overall progress of

the stock is declining.

Page 38: Nissan Stocks - Data Analysis

38

Measures of Central Tendency

Equation: ∑

=

Mean: $16.22069969

Median: $17.15

Mode: $16.45

Therefore, the average Open Stock Value for the five years is $16.22. The middle number is

$17.15 and the most frequently occuring value is $16.45. With a range going from $5 up to $23

these numbers are pretty high on the scale.

Page 39: Nissan Stocks - Data Analysis

39

Probability Distribution Formation

In conclusion, looking at this histogram we are able to analyze the different ranges of

data for the open stock values. The stock prices range from $6-22.99 which gives a pretty wide

range for the year. Just at a quick glance it is easy to see that the most frequent stock values

range from $17-19.99 (538 occurences), with $14-16.99 not too far behind (360 occurences).

The least occuring interval range $8-10.99 with only 59 occurences. With such a wide range of

stock values it shows that the open stock values had some inconsistency over the five years.

Mean: $14.74411067

Median: $16.08

Mode: $18.36

0100200300400500600

# o

f O

ccu

ren

ces

Intervals ($)

2008-2012 Nissan Open Distribution

Page 40: Nissan Stocks - Data Analysis

40

PART D: WRITTEN REPORT ON

MATHEMATICAL UNDERSTANDING OF MATERIAL

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41

By analyzing all of nissans stocks over the past five years, I’ve had the opportunity to

gain knowledge on the company and would not suggest investing into the NSANY stock. Before

doing this assignment I would have assumed Nissan was a good investment since their cars sell

well. Having done another stock project in the past, however, it is not a surprise to see the

fluxuation of stock prices with several declines and increases.

The line of best fit indicates that the approximate initial stock value was $19.90. The

initial stock value was lower then the year end of $21.48. Overall at the end of the five-year span

the stock value has an ending increased value. Even though the value has increased there is a

negative slope. The lowest price over the five years was $5.65 and the highest was $21.94.

Although it had many increases and drops, the Nissan stock managed to come back up to an

acceptable value. Using the data we can see that their worst year was 2009 since the data was

inconsistent and dropped significantally, and their best year was 2011 as the value finally

increased after a two-year decline.

Over the Five years the greatest range of stocks were approximately $17-$20 which is on

the higher end of their fluxuating prices. This is positive because although not completely

consistent, for some time throughout the past five years Nissan could have been considered a

good buy. Looking at the future prediction for a decline is what makes it more of a negative

stock.

By investing in the stock market, any investor should only be buying knowing about the

risk they are putting their money into. The market changes daily and if someone only invests in

one field of the economy they will either profit a lot quickly or lose everything all at once. In

order to keep balance it’s suggested that someone invest in multiple stocks not related to

eachother.

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42

PART E: APPENDICES, ROUGH MATHEMATICAL WORK,

MISCELLANEOUS AND BIBLIOGRAPHY

Page 43: Nissan Stocks - Data Analysis

43

Bibliography

“Historical Prices.” Yahoo Finance. n.a. n.d. Web. 3 Sept. 2013.

“Message/Vision.” Nissan-global. Carlos Ghosn, n.d. Web. 15 Sept. 2013.

“Nissan Work.” Coroflot. Nick Coughlan. 17 Jan. 2009. 25 Nov. 2013.

“Production Nissan Juke-R Sketches.” Auto Evolution. Mihnea Radu. 8 Aug. 2012. 25 Nov.

2013.