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Statistics is fun! :p
It's 2:30am and I've just finished up a semester-portfolio assignment for my statistics class ECON7300 - Statistics for Business and Economics. (Fun all day long!)
Think my assignment is holding up alright... At least until the last few questions, which were finished on the wrong side of midnight! My writing seems to suffer a certain drop in quality as the day passes by and a number of unnecessary words and a fair bit of crap sneak into my language!
The course isn't really all that exciting, but you can't say I haven't learnt anything... The main thing the teaching staff has tried to instill in us is how to analyse the relationship between two or more variables.
To demonstrate my knowledge, I shall perform a regression analysis on time's effect on my above mentioned tendency to "crap on" as the day fades away. Such an analysis goes straight to the heart of the assignment I just finished!
I made observations every 15 minutes as to the quality of my writing. The observations were made over a time period of 7.5 hours late at night. Good writing was awarded with points on the lower end of a scale from 1 to 15. Writing with much crap in it scored higher on the scale.
A linear relationship was assumed, and the population model was, therefore,
Y = B1 + B2X + E or
Crapping on factor = B1 + B2(Time) + Error term
Where B1 is the regression constant and B2 is the correlation coefficient. In other words, B1 is the level of crapping on at time 0, while B2 is the increase in the "crapping-on factor" of my writing for each time period.
For the purpose of testing the crapping-on model for significance, the following hypotheses were set up:
H0: B2 equals 0
H1: B2 not equal to 0
If the null hypothesis (H0) can be rejected at a 5% significance level (95% confidence level), it is reasonable to assume that the crapping on factor does change over time and that the two variables, therefore, are related.
The data was fed into Minitab 14, a stats software. It returned the following analysis of the "Crapping on factor" as a function of time:
Regression Analysis: Crapping on factor versus Time
The regression equation is
Crapping on factor = - 1.33 + 0.350 Time
Predictor Coef SE Coef T P
Constant -1.3310 0.6281 -2.12 0.043
Time 0.35039 0.03538 9.90 0.000
S = 1.67725 R-Sq = 77.8% R-Sq(adj) = 77.0%
As you probably already understand, since the P-value of time is less than 0.05 (the significance level), the null hypothesis can be rejected. There IS a correlation between the quality of my writing and time of the day. :D
What the regression analysis says, is that the quality of my writing - as ranked on the scale from 1-15, 15 being utter dumbness - drops over time. More specifically, it says that its crapness score increased by 0.35 points every 15 minutes for the 7.5 hours of observation.
Before observations started, my expected crapness level was -1.331 - or, in other words, so good that it was off the scale. Sadly, at time 30 (the last observation), my level of crap writing would have gone up to 9.17.
The purpose of all of this? Nothing really... Just to prove myself and my regression analysis right. At the moment my crap factor should be about 11.27, which seems to be quite correct considering what I just managed to write here! :o)
Posted by Marius Berg Askildsen
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