## Monday, June 11, 2012

### Ch3 Math Finance Part 2

Ch3 Project Voice Thread Link by Thanh, Min Ying and Lan: Future Value of Annuity

### Interest Compound Continuously

Interest Compounded Continuously

## Friday, June 8, 2012

### Chapter 2 Project

According to zillow.com, the property taxes of my grandparent's house is \$4,778 as of June,2011. The tax was \$4,524  when my family moved in during October 2008.
• To find the model, you go to STAT ---> EDIT---> Plug in X & Y values. The X values would be from 2004-2011 but I type in #1-8 represent years. The Y values would be the property taxes. Then I found Quart Reg fits the best after I tried all four Reg ( Linear, Quad, Cubic, Quart) because R^2 is closet to 1.
• My house property taxes will not be \$100,000 because the maximum in \$4,800.
• The prediction can be changed if the value of the house increases.

### Chapter 2 Project

From Zillow.com, I found out that the house I live in was worth 332,000 in October, 2009, which was when I moved in. To find out the best regression model, i use the data I collected on Zillow and plugged it into my calculator. I went through all the different regression models, like cubic, linear, quadratic, etc. I found out that quartic regression is the most accurate.
The equation is 1.38x^4-24.588x^3+121.630x^2-107.510x+270.720.
In the future, the house will never drop to 100,000 because the minimum value is \$114,500.
The prediction can change if the economy drops even further, which means houses may go down in price.

## Thursday, June 7, 2012

### Ch. 2 Project

From the data that we get from Zillow.com, I find out that the house I live in worth 546,000 at Jun, 2004. To find the best fit model to predict the price of the house at certain time period. So I put all my data into the calculator by pushing STATS and punching in the numbers, then I press STATS again to try out the buttons that make the best formula, like linear regression, Quadratic regression, Cubic regression, Quartic regression, and I found out that Cubic regression is the best fit equation because r^2 = .9427, so this is the only equation that is closest to 1. So the equation is 1.55x^3 + -33.4x^2 +189.82x + 246.6 . In the future, this house will never drop to 100,000 dollars because the minimum value is 357.23k. This equation can be change when  the government change or tax change , and other factors.

### Chapter 2 Project

For the Chapter 2 project, I learned that my house is currently worth \$180,200 on zillow.com but a few years ago, before I moved in, my house was worth up to \$519,000.
I then used my calculator to find a linear regression formula to calculate how long or when my house will reach a certain price and I learned that in 2017, my house can reach \$100,000. Some ways that can change my prediction would be if this community becomes richer and safer, the price of the house would definitely increase.

### Chapter 2 Project

Using the information from zillow.com, my house is worth \$244,400 today, and was worth \$368,000 in 2004 when we first moved in. To create this model, you need to enter the data to the STAT table. X is equal to the years starting from 2002-2011 (represented as 1-10 respectively). Y is equal to the value of the house in thousands during each year. After entering the data and checking through the 4 regression models (linear, quad, cubic,and quart), i found that the quartic regression had fit my model the best with r^2=.8265742, which was closest than all the other regressions models. The quartic regression is Y=1.197898X^4 -25.626748X^3 +168.101253X^2 -345.119463X +573.583334. the value of this house will not reach \$100k. The minimum value is \$251k. My prediction can change if the house gets damaged or if the value of the land goes down, causing the price of the house to drop.

### Chapter 2 project

itled.png" imageanchor="1" style=""> href="http://4.bp.blogspot.com/-8P8UokR7-F8/T9GJReWLQII/AAAAAAAAAEQ/QmoFKQuJ1gw/s1600/Unt According to Zillow, the house my family and I moved into was worth \$509,000 during the year 2004. I used my calculator to find the model by entering my X and Y values into the STATS table. My X are the years and my Y are the value of the house. My linear regression equation is y=54466.4+-26.72x with the Rate of .5319350662. My house will reach the value of \$100,000 until the year 2023. The yearly depreciation of the house is \$17,000. Some things that could happen that could change the value is the increase in violence or the amount of people moving in and out of the neighborhood.

### Ch2 Project

Zillow.com explains that the house I currently live in is worth \$225,100. In 1996, when we moved in it was worth about \$484,000. To find the graph I used X for the number of years and Y for the value. Then I used the quartic regression, because r2 =0.96 which was the closest compared to other regression models. The quartic regression is y= 435.17x4-3491771.47x3+1.05x2-7.04, the house could reach a value of \$100,000 in 2027. The value of the house could change depending on various factors, such as the color of the paint the other houses in the neighborhood has.

### Ch 2 Project

Zillow.com has shown that my house \$513k when we moved in on May, 2010. The price of it now (June 2012) is worth around \$420k. To find what kind of regression model I used for the that, I plugged the X and Y values into the stats table. Then I clicked Stat > Calc > Lin Reg / Quad Reg / Cubic Reg / Cubic Reg. Then I entered one of those regression and clicked Y1 and Y2 and entered again. Then i can see the numbers for each regression. To see which model was best, I chose the one that was closest to 1 for R^2 and it was the Quartic Regression, so I chose that as my equation.

My house value cannot reach \$100k as the minimum house price was \$379k.
My prediction can be changed if prices need to be dropped so it becomes more affordable to the general population.

### Ch2 Project

According to Zillows, my house is now worth \$,242,300 as of June 03, 2012. I moved into this house around June, 2008 and it was worth around \$484,000. To find the regression equation for the data, i plugged them into a graphing calculator and found that the Quartic Regression best fits the data because the coefficient of determination was the highest (r^2 = 0.7419).
The Quartic Regression if got from my data is y = 0.4659x^4 - 10.42094x^3 + 63.9653x^2 - 69.3296 + 353.4242.
My house's value will never reach \$100,000 because the minimum value of my house is \$275,950 and my prediction can be changed if my neighborhood starts to improve and the prices of nearby houses rise so my house would probably rise along with them.

### Chapter 2 Project

Using the information from zillow.com, the house I live in is now worth \$282,000 when I first moved in at March, 2012 . To find the model, I type in #1-10 which represent years 2002-2011; then I put the past values from 2002 through 2011 in thousands of dollars as Y. Next, i tried all four regression models(Linear, Quadratic, Cubic, Quartic) to see which model fits the best, and it turns out that Quartic regression is most accurate because the r^2 is 0.9466850693, which is closer to 1 out of the other three. My Quartic regression equation is: y= .7152x^4 + -15.47^3 + 98.25x^2 + -165.46x + 393.75. This house will never reach the value of \$100,000 because the minimum value is \$247,000.

The prediction of the quartic model can change if the economy, neighborhood, or conditions of the house are bad. This would to lead to downfall in prices.

### Chapter 2

According to the data provided in zillow the house that I moved into in 2002 was worth \$230,000. To find the model you go to stat then edit then plug in your x values and your y values. The x values would be from 2002-2011 then the y values are from \$230,000-\$533,000. The quadratic regression was the best because the R was closer to 1. The quadratic regression model was Y = .47115384615439x^4+ -3779.3265345809x^3+11368322.761959x^2+-15198295709.015x+7619451108445.9. The house that I live in will never be worth 100,000 because the minimum value is 230,000. A factor that can affect the value of my house would be if more people move into the area or if there is another recession.

## Wednesday, June 6, 2012

### Chapter 2 Project.

According to the data provided from Zillow, the house I reside now has the worth of \$499,000 when I moved in during October of 2011. To be able to find the model, I'll first have to enter it on the STATS table. My x is years: 2003-2012, while my y is the value of the house: \$358K-\$467K. My linear regression equation is: y=-2.193.939394x+4840533.333. R=.0809874044. My house would not reach the value of \$100K until 2,161 years. I moved to my house for nearly only a year, and the yearly appreciation would be \$32,000. If more people moved to my neighborhood, then the house prices/value would possibly decrease.

## Sunday, April 22, 2012

### Chapter 2 Project

The current Zestimate price of the house I am living in is \$273,300. My grandpa first bought this house in 1988 for \$152,000.

Linear Equation : y = -22466.67x + 551066.67
r2 = .4484
Quadratic Equation : y = -6886.36x2 + 53283.33x + 399566.67
r2  = .7181
Cubic Equation :  y = 2430.85x3 - 466995.338x2 + 238270.78 + 191000
r2  = .9146
Quartic Equation : y = 110.72x4 - 5.05x3 - 29168.99x2 + 189552.84x + 229000
r2  = .9168

By looking at the four different equations, the quartic equation has the strongest linear correlation because it is closer to 1. The average yearly appreciation of the house would be \$6,217.39 per year. In about 20 years, the price of my current house would be \$100,000. Any negative events that will happen in the neighborhood could affect the value of the house since nobody would want to live in a dangerous and unsafe area.

## Tuesday, April 17, 2012

### CH2 Project

According to the information from zillow.com, the home I live in now is worth \$233,000 when I first move in at June in 2009. To find the model, I type in the years for X in the calculator STAT table with 2002 as year 1, 2003 as year 2 and so on; then I put the past values from 2002 through 2011 in thousands of dollars as Y. Next I turn STAT Plot and Diagnostic on, so now I could try applying different regressions with my data from zillow.com. It turn out that quartic regression model,y=.5304487179x^4 - 10.26330614x^3 + 55.10678904x^2 - 63.99339549x +308.9166667, fit the most because coefficient of determination (r^2) is 0.8886096037, which is closer to 1 than the other. To see the graph I set the window to [0,11] by [0,500]. I put in y=100 to find out when will the value be 100,000 but the model did not intersect with the line y=100 with the minimum value \$192510.60 at x=9.2 (2010).
In my opinion, the prediction from the quartic model could be change if the government lower the number of immigrants from entering U.S. in the future.If that happen oakland house values will drop from the decreasing demands of rent housing.

## Thursday, April 5, 2012

Please Go HERE for instructions on the CH 2 Project

Option 1

We are doing Option 2 in class tomorrow.

## Wednesday, March 21, 2012

### Proofs

Trigonometric Proof
Prove sinu + sinv = 2sin (u+v/2) cos (u-v/2)
 1. 2sin (u+v/2) cos (u-v/2) 1. Given 2. sinu cosv = ½ (sin (u+v) + sin (u-v)) 2. This is the product-to-sum formula, ½ (sin (u+v) + sin (u-v)) that was also given. 3. 2 x ½ (sin (u+v – (u-v)/s) + sin (u+v+u-v)/2) 3. Plug in the equation 2sin (u+v/2) cos (u-v/2) 4. 1 (sin (2v/2) + sin (2u/2)) 4. Distributive property of multiplication and combine like terms. 5. 1 (sinv + sinu) = sinv + sinu 5. Simplify!
Paragraph Proofs: I would like to prove that sinu + sinv = 2sin (u+v/2) cos (u-v/2). I was given that sinu cosv = ½ (sin (u+v) + sin (u-v)) so I plugged 2sin (u+v/2) cos (u-v/2) into ½ (sin (u+v) + sin (u-v)) and I got 2 x ½ (sin (u+v – (u-v)/s) + sin (u+v+u-v)/2). Then I used the distributive property of multiplication and combined like terms to get 1 (sin (2v/2) + sin (2u/2)) and lastly, I simplified the equation to get sinv + sinu.