Herman,+S

Data CT

 * Brainstorming:**
 * summer vacations vs. skin cancer rates
 * university digrees, diplomas & certificates granted vs. unemployment rate
 * marijuana and alcohol consumption vs. number of high school graduates
 * average household income vs. grade average



Does the number of university digrees, diplomas, and certificates granted (independant variable) in Canada have an affect on the unemployment rate (dependant variable) in the years 2004 to 2008 in Canada?
 * Question:**

I believe there will be a negative moderate correlation between the two variables. As more people graduate from university, it is likely they are going to obtaina job soon after. Therefore, the unemployment rate should go down. "x" increases as "y" decreases.
 * Hypothesis:**

As the majority of our class will be going to university next year, I was curious to see if going to university really affected the unemployment rate. University will most likey lead you to a better job and/or career, but will not going lead you to no career at all? I think not! Apprenticeships, colleges, and other programs can lead into many future options. There was recently a recession across Canada. Did those who went to university get to keep their jobs? Or was it fair game for all?
 * Background Info:**

Number of digrees, diplomas, and certificates awarded:
 * Raw DATA**


 * Year ||  Number Awarded (Canada)  ||
 * 2004 || 211 902  ||
 * 2005 || 216 240  ||
 * 2006 || 227 085  ||
 * 2007 || 242 787  ||
 * 2008 || 244 380  ||
 *  Year ||  Number Awarded (Ontario)  ||
 * 2004 ||  80 436 ||
 * 2005 ||  84 138 ||
 * 2006 ||  89 244 ||
 * 2007 ||  102 153 ||
 * 2008 ||  99 387 ||

Unemployment Rate:


 * Year ||  Percent of Population (Canada)  ||
 * 2004 || 7.2  ||
 * 2005 || 6.8  ||
 * 2006 || 6.3  ||
 * 2007 || 6.0  ||
 * 2008 || 6.1  ||


 * Year ||  Percent of Population (Ontario)  ||
 * 2004 || 6.8  ||
 * 2005 || 6.6  ||
 * 2006 || 6.3  ||
 * 2007 || 6.4  ||
 * 2008 || 6.5  ||

All of the data used was collected through Statistics Canada. The data may be skewed due to a voluntary response sample. The data is supposed to represent all of Canada, but there is a chance that some surveys were not returned or taken. A non- response bias could also be a factor in the data if some regions of Canada were under- represented. For the unemployment data, a response bias could have occured. Canadians could be ashamed of their situation, leading them to gie false answers.
 * Sampling Technique and Bias:**

**ONE VARIABLE CALCULATIONS**
**Mean: ** //Canada // µ= __1142394__ 5 =**228 478.8**

//Ontario // µ= __455358__ 5 =**91 071.6**


 * No Mode**

**<span style="font-family: 'Arial','sans-serif'; font-size: 13pt;">Median: ** //<span style="font-family: 'Arial','sans-serif'; font-size: 12pt;">Canada //<span style="font-family: 'Arial','sans-serif'; font-size: 12pt;"> – **227 085** //<span style="font-family: 'Arial','sans-serif'; font-size: 12pt;">Ontario //<span style="font-family: 'Arial','sans-serif'; font-size: 12pt;"> – **89 244**

**<span style="font-family: 'Arial','sans-serif'; font-size: 13pt;">Standard Deviation: ** //<span style="font-family: 'Arial','sans-serif'; font-size: 12pt; line-height: 115%;">Canada // <span style="font-family: 'Arial','sans-serif'; font-size: 12pt; line-height: 115%;">ơ =√ __ 884094356 __ <span style="color: black; font-family: Calibri; font-size: 12pt; line-height: 115%; margin: 0cm 0cm 10pt;">5 <span style="color: black; font-family: Calibri; font-size: 12pt; line-height: 115%; margin: 0cm 0cm 10pt;">=√176818871.2 <span style="color: black; font-family: Calibri; font-size: 12pt; line-height: 115%; margin: 0cm 0cm 10pt;">=**13 297.33**

// Ontario // <span style="font-family: 'Arial','sans-serif'; font-size: 12pt; line-height: 115%; margin: 0cm 0cm 10pt;">ơ = √__356474221__ <span style="font-family: 'Arial','sans-serif'; font-size: 12pt; line-height: 115%; margin: 0cm 0cm 10pt;">5 <span style="font-family: 'Arial','sans-serif'; font-size: 12pt; line-height: 115%; margin: 0cm 0cm 10pt;">=√71294844.2 <span style="font-family: 'Arial','sans-serif'; font-size: 12pt; line-height: 115%; margin: 0cm 0cm 10pt;">=**8 443.63**

<span style="font-family: 'Arial','sans-serif'; font-size: 12pt; line-height: 115%; margin: 0cm 0cm 10pt;">In Canada for the years of 2004 to 2008, the number of digrees, diplomas, and certificates awarded has a range of 32 478 (244 380 - 211 902). <span style="font-family: 'Arial','sans-serif'; font-size: 12pt; line-height: 115%; margin: 0cm 0cm 10pt;">Likewise, Ontario has a range of 21 717 (102 153 - 80 436).
 * TWO VARIABLE CALCULATIONS**

Canada: r = __n____Σ____xy – (____Σ____x)(____Σ____y)__ _ √[nΣx₂ - (Σx)₂][nΣy₂ - (Σy)₂] = __ (5)(73742.019) – (1142394)(0.324) _ __ √[(5)(261896904198) – (1142394)₂][(5)(0.021098) – (0.324)₂]  = __368710.095 – 370135.656__ _  √[1309484520990 – 1305064051236][0.10549 – 0.104976]  = __-1425.561__ _  √(4420469754)(0.000514)  = __-1425.561__ _  √2272121.453556  = __-1425.561__ _  1507.355782009012  = -0.9457

STRONG NEGATIVE CORRELATION

Ontario: r = __n____Σ____xy – (____Σ____x)(____Σ____y)__ _ √[nΣx₂ - (Σx)₂][nΣy₂ - (Σy)₂] = __(5)(29643.075) – (455358)(0.326)__ _ √[(5)(41826655854) – (455358)₂][(5)(0.02127) – (0.326)₂]   = __ 148215.375 – 148446.708 _ __  √[209133279270 – 207350908164][0.10635 – 0.0106276]  = __-231.333__ _  √(1782371106)(0.0957224)  = __-231.333__ _  √170612839.9569744  = __-231.333__ _  13061.88500779939  = -0.0177

Linear Regression Canada a = __n____Σ____xy –__ __Σ____x____Σ____y__ nΣx₂ - (Σx)₂ = __(5)(73742.019) – (1142394)(0.324)__ (5)(261896904198) – (1142394)₂  =__368710.095 – 370135.656__  1309484520990 – 1305064051236  = __-1425.561__  4420469754  = -3.2249

b = y-ax =(0.324/5) – (-3.2249)(1142394/5) = 0.0648 + 736821.28212  = 736821.35

** y = -3.22x + 736821.35 **

Ontario

a = __n____Σ____xy –__ __Σ____x____Σ____y__ nΣx₂ - (Σx)₂ = __(5)(29643.075) – (455358)(0.326)__ (5)(41826655854) – (455358)₂  = __148215.375 – 148446.708__  209133279270 – 207350908164  = __-231.333__  1782371106  = -1.2979

b = y – ax = (0.326/5) – (-1.2979)(455358/5) =0.0652 + 118201.82964 = 118201.9

My hypothesis was incorrect. There was a strong negative correlation amongst the data across Canada, and a weak negative correlation in Ontario. Ontario can be looked at as a sample of Canada or as a population itself. Looking at it as a sample of Canada the data would not be as accurate. Resulting in a weaker correlation. There are external factors that affect the unemployment rate that I did not take into consideration throughout my analysis. These include; college graduates, appreticeships, and other programs that allow job opportunities.
 * y = -1.3x + 118201.9**
 * CONCLUSION**


 * Source:**

Unemployment Rate, Canada. (2010, May 26). In //Statistics Canada//. Retrieved December 6, 2010

What are the adverse effects of unemployment?. (2009, July 11). In //e-notes//. Retrieved December 6, 2010

University degrees, diplomas and certificates granted by sex, by province. (2010, July 14). In Statistics Canada. Retrieved December 26, 2010