Tuesday, 7 April 2015

Oil Prices





Oil Prices

For this assignment, I decided to talk about oil prices. First of all, I would like to point out the fact that oil is an essential resource in our economy. Also oil is one of the most important industries in Alberta.
 
Oil Prices Chart

In the following table, we can see the oil prices for the last thirteen months including April. By looking at the data we can see that there is a significant difference between last year and this year price. The highest price was on June 1, 2014 (Month 2) at $105.37 per barrel. The lowest price was on March 1, 2015 (Month 11) at $47.60 per barrel. The average price was $76.49 per barrel.

Month
Date
Price
0
2014-04-01
 $   99.74
1
2014-05-01
 $ 102.71
2
2014-06-01
 $ 105.37
3
2014-07-01
 $   98.17
4
2014-08-01
 $   95.96
5
2014-09-01
 $   91.16
6
2014-10-01
 $   80.26
7
2014-11-01
 $   66.64
8
2014-12-01
 $   54.96
9
2015-01-01
 $   50.07
10
2015-02-01
 $   52.14
11
2015-03-01
 $   47.60
12
2015-04-01
 $   49.53

After analyzing the prices on the table for the indicated months it is obvious that the price has dropped by $50.21 per barrel in the last year. This has a negative impact to the world’s economy because most industries relies on this resource.

Oil Prices Equation

Equation Type: Cubic Regression


Y = 0.1565x^3  +(-2.9026)x^2+ 8.3058x + 98.5614



The graph above shows the cubic function f(x) = 0.1565x^3  +(-2.9026)x^2+ 8.3058x + 98.5614. This function shows the decrease in oil price. We can see that the cubic regression is the one that best describes the data. There were many factors that caused the oil price to drop including supply in terms of output, access to future supply, and oil demand. The graph shows that on April 2014 the price per barrel was about $105.37/Barrel. By the end of 2014 the oil price went down to $54.96/Barrel. On March 2015, the price for oil hit its lowest mark in the past 7 years with $47.60/Barrel. Based on the graph, since the price reached the lowest price point we can predict that the price will bounce back up.


Change in price Chart

The following table is the change in dollars of the oil price for the past 13 months including April 2015. In the data, between July 2014 and January 2015 the price gap was -$55.30. This significant change in price worries the oil industry, mainly because profits will decrease and they might have to cut costs by laying off people, shutting down operations, and cancelling projects.   



Month
Date
Change in $
0
2014-04-01

1
2014-05-01
 $            2.97
2
2014-06-01
 $            2.66
3
2014-07-01
-$           7.20
4
2014-08-01
-$          2.21
5
2014-09-01
-$           4.80
6
2014-10-01
-$        10.90
7
2014-11-01
-$           13.62
8
2014-12-01
-$        11.68
9
2015-01-01
-$           4.89
10
2015-02-01
 $            2.07
11
2015-03-01
-$           4.54
12
2015-04-01
 $            1.93

Change in Dollars

Equation type: Cubic regression

Y = 0.0314x^3+(-0.2529)x^2  +(-1.4142)x + 2.5639


The graph above shows the cubic function f(x) =  0.0314x^3+(-0.2529)x^2  +(-1.4142)x + 2.5639 . After June 2014, there was an oil price constant decline until February 2015 where there was a little increase of $2.07. The price went down again for the month of March 2015, then on the beginning of April the price increased by $1.93. It is expected that the oil price should increase within the upcoming months.   


Pros & Cons of Current Oil Price trend




Pros
  • Due to the low barrel price, gas prices will likely tend to go down.
  • Products such as groceries, goods, etc. will tend to be cheaper to transport due to the low price in oil.
  • Low oil prices also help to lower cost of living.

Cons
  • Lay-offs in the oil industry.
  • Weakens economies relying on the oil industry.
  • Research for new energies started by Oil companies might not have enough profits to grant research. 

Conclusion

After reviewing and doing all the required analysis, we can conclude that oil prices have an impact in our economy and our daily lives. The low oil price has affected Alberta in general negatively. People are losing their jobs, local oil companies are losing profit, and the city’s economy is getting weaker. According to the graphs and the analysis made, we can deduct that they oil price will go up hopefully by the end of the year.

References






Thursday, 2 April 2015

Population of China


China

World's Most Populated Country



China's population as of 2015 is 1.4 billion making it the world's most populous country. Using provided data demonstrating growth of China's population since 1960 we will select best equation which describes population growth until present day.

Table 1. Raw Data

Line 1 Years after 1960
Line 2 Population in Millions
0
667
5
715
10
818
15
916
20
981
25
1051
30
1135
35
1204
40
1262
45
1303
50
1337
55
1370


Provided data was loaded into a graphing calculator to perform regression analysis. Four different equation types were tested:

  1. Cubic regression
  2. Quadratic regression
  3. Exponential regression
  4. Linear regression

1. Cubic Regression Graph





Cubic Regression Equation:

y = ax3 + bx2 + cx + d
y = -0.0024107744x3 + 0.0845532246x2 + 15.53260813x + 656.3589744


Y-intercept: 656
Number of X-intercepts: 1


2. Quadratic Regression Graph





Quadratic Regression Equation

y = ax2 + bx + c
y = -0.1143356643x2 + 19.72132867x + 641.4423077

Y-intercept: 641
Number of X-intercepts: 2



3. Exponential Regression Graph





Exponential Regression Equation

y = abx
y = 717.0066508 1.013448475x

Y-intercept: 717
Number of X-intercepts: 0




4. Linear Regression Graph




Linear Regression Graph

y = ax + b
y = 13.43286713x + 693.8461538

Y-intercept: 694
Number of X-intercepts: 1


Table 2: Pros and Cons



Pros
Cons
Cubic
Fits most data points
Does not fit 2 data points
Quadratic
Fits 2nd most data points
Does not fit 4 data points
Exponential
None
Only fits 2 data points
Linear
None
Only fits 2 data points



China's Future Population

Predictions and Extrapolations


This data collected from a Wikipedia source shows that China's population is expected to begin declining by 2040.

Table 3: China's future population - data from Wikipedia source


Line 1 Year
Line 2 Population in Millions
2020
1387
2030
1393
2040
1360
2050
1295
2060
1211
2070
1125
2080
1048
2090
984
2100
941


Previously found Cubic Regression equation was applied to same Year points - 60 to 120 year after 1960. Resulting Population Data points can be found in table below.


Table 4: China's future population as predicted by my Cubic Regression equation


Line 1 Years after 1960
Line 2 Population in Millions
60 (2020)
1372
70 (2030)
1331
80 (2040)
1206
90 (2050)
982
100 (2060)
644
110 (2070)
179
120 (2080)
- 428
130 (2090)
- 1192
140 (2100)
- 2127


This data predicts a drastic decline of China's future population which does not fit statistical prediction obtained from Wikipedia source.

Next I applied previously found Quadratic Regression equation in the same manner. Resulting Population Data points can be found in table below:

Table 5: China's future population as predicted by my Quadratic Regression equation


Line 1 Years after 1960
Line 2 Population in Millions
60 (2020)
1413
70 (2030)
1462
80 (2040)
1487
90 (2050)
1490
100 (2060)
1470
110 (2070)
1427
120 (2080)
1362
130 (2090)
1273
140 (2100)
1161


This data indicates that China's future population will continue to increase until a peak in 2050 after which it will start to decline again. This is a reasonable prediction.






Conclusions

In years from 1960 to 2015 Chinese population has been increasing. According to various predictions China's population growth will slow down and reverse in future. Results of my Quadratic Regression (see Table 5) equation predicts this trend to reverse in 2050s with China's population begging to decline slowly. Results of my Cubic Regression (see Table 4) predicts China's population begging to sharply decline in 2020s. Lastly data obtained from Wikipedia source indicates that statistics predicts China's population growth to reverse in 2030s.

References


  • China's population growth (Table 1): http://countrymeters.info/en/china See table: China population history
  • China's future population (Table 3): http://en.wikipedia.org/wiki/Demographics_of_China See: Population Projection, United Nations 2010 estimate.



Monday, 16 March 2015



Math 30-2 Research Project


The purpose of the research project in Math 30-2 is to gain an appreciation for mathematics in current events. You will research statistical data then analyze and present your findings within the Math 30-2 Project Blog. This project is worth 5% of your class grade.

Choose only 1 of the projects listed in the project link.  If you have another idea, pass it by me before you begin.The marking rubric is shown at the end of the project link document.

To achieve a great mark:
  • include raw data
  • do a regression analysis
  • include a graph plotting your data and drawing your best fit regression curve
  • present pros and cons with support
  • make some conclusions
  • include or references
  • present in a neat and orderly fashion (pictures are always a nice addition)

Your project is worth 4% of your grade and is due to be posted by Tuesday December 1. If peers make a comment or ask a question, maintain your own post by answering.

The remaining 1% of the grade is your responses to your peers posts.  At least four thoughtful and reflective comments are required for the additional 1%.  Responses to peer posts are required by the last day of class: Tuesday December 8.



Monday, 1 December 2014

Golf Club Trajectory

What Is the Loft of a golf club?

Loft angles are expressed in degrees with respect to vertical rather than the ground. The more highly lofted a club is, the higher the golf ball will go on impact. The below diagram represents the loft angle of a club blade and the trajectory angle it has.

                                                                                   



























So what are the official loft angle for each golf club?


There aren't any official values. Manufacturers are allowed to set the angles to whatever they wish. By slightly reducing the loft angle of a club, the ball travels farther. In this sport, distance sells. In the industry they call it creep when changing the loft angle for more distance. Below is a chart that shows the typical loft angles for a set of irons.



Club
Loft Degree
4 Iron
25
5 Iron
28
6 Iron
31
7 Iron
34
8 Iron
37
9 Iron
41
Pitching Wedge
45
Gap Wedge
50
Sand Wedge
55
Lob Wedge
60





Mean x (x̄): 5.5
Mean y (ȳ): 40.6
Intercept (a): 19.4
Slope (b): 3.8545454545455
Regression line equation: y=19.4+3.8545454545455x
*club 1= 4 iron, club 2=5 iron...ect

When looking at the graph, we can conclude that Club 1 (4 iron) has the smallest degree of loft and Club 10 (Lob wedge) has the largest degree of loft.



What are the official distances with each golf club?


Club
Distance (yards)
4 Iron
170
5 Iron                       
160
6 Iron
150
7 Iron
140
8 Iron
130
9 Iron
120
Pitching Wedge
105
Gap Wedge
90
Sand Wedge
70
Lob Wedge
40



Sample size: 10
Mean x (x̄): 5.5
Mean y (ȳ): 117.5
Intercept (a): 191.33333333333
Slope (b): -13.424242424242
Regression line equation: y=191.33333333333-13.424242424242x
*club 1= 4 iron, club 2= 5 iron...ect

From this graph we can conclude that Club 1 (4 iron) can hit the ball the farthest out of all the clubs (approx 170 yards.) We can also confirm that Club 10 (Lob wedge) has the shortest range out of all the clubs (approx 40 yards.) When comparing this graph to the above one, we can get an idea of the club loft vs. its distance. For example, Club 1 (4 Iron), has the lowest possible loft degree of 25 but in return it can be used to deliver the longest distance of all the clubs. The 4 iron, when used, is able to hit the golf ball the farthest out of any irons. If we take a look at Club 10 (Lob wedge), it has the absolute highest degree of loft (60 degree) out of all the irons but the shortest distance (40 yards.) The lob wedge when used has the shortest range out of all the irons.

When trying to determine what club to use, it all depends on your yardage to the hole. If you have a far shot that is around; 170-200 yards then pick the 4 iron, if your only 100 yards away from the pin then the pitching wedge would applicable for this situation. If you would like to hit a longer shot, then a lower loft degree on the club face is needed. For a shorter shot, a higher degree of loft will need to be used to launch the ball high and controlled instead of long.

There are two regulations in golf club production, 1. Form and Make of clubs, and 2. Foreign Materials. These regulations are needed so that no club has the potential to out perform another club based on what it is made of. If a producer added some foreign materials in or on the club face, and a player was able to hit farther and more accurate, the player and the producer would then be investigated by the USGA (United States Golf Association.)



Dylan Pescod



Research:

http://www.leaderboard.com/loftinfo.htm
http://www.alcula.com/calculators/statistics/linear-regression/
http://www.usga.org/Rule-Books/Rules-on-Clubs-and-Balls/Rule-4-%E2%80%93-Clubs/