Neil's Stats Blog

nmatheson — Wed, 20 May 2009 01:49:58 +0000

We can also find out how to calculate the postmolt size by finding the slope of the regression line.

= 1.1 mm/mm

We can also use a residual quantile comparison plot to determine the difference between the crab’s actual premolt size and the regression line that predicted it.

The residual SD can also be computed fairly easily

nmatheson — Wed, 20 May 2009 01:35:20 +0000

For the study of crab molt sizes we use a linear model to try to predict the size of a carapice based off of the premolt size. The correlations are highly linear so we can use what is called a correlation coefficient. A correlation coefficient of +1 or -1 indicates a very strong linear correlation.

Here is the equation for the coefficient

for our model

r = 0.9808

This means we have an excellent correlation

Here is a scatterplot of both molts

Dungeness Crab Growth

nmatheson — Wed, 20 May 2009 00:58:06 +0000

Dungeness crabs are commercially fished in the mid winter to early summer months, off the Pacific Coast of North America. Our job here is to study the measurements of the premolt shell size and try to make an assertation as to the postmolt size of the crab shell. The study was taken place during 3 seasons. The first were in 1981 and 1982, and the third was in 1992. Over 12,000 crabs were obtained altogether.

Here is a description of the data.

Variable	Description
presz	Premolt carapace size in millimeters
postsz	Postmolt carapace size in millimeters
incr	Increment = postmolt size – premolt size
year	Year (81=1981)
lf	Measurement site 0=field, 1=lab

nmatheson — Wed, 20 May 2009 00:52:00 +0000

Here we find the distribution of palindrome counts for the intervals of 400 pairs of 294 palindromes.

We also show the histogram graph of the locations of the palindrome base pairs below. This allows us to see how the palindromes are distributed throughout their locations, each in a semi randomly generated spot.

Patterns in DNA

nmatheson — Wed, 20 May 2009 00:25:56 +0000

Here we study the patterns in aspecific strain of a virus. We are analyzing the data and looking for palindromes. We start by looking at a scatter plot of the data.

As we can see there are breaks in the palindrome distribution of DNA patterns. We want to know how to find these breaks. By using the Poisson Distribution we can figure this out.

= P(No hits in an interval of length t)

nmatheson — Tue, 19 May 2009 23:18:07 +0000

Taken from the a page in the text we find the estimator for the standard error is :

We can use this to tell the size of the deviation of the estimator from its expected value.

Together with equation for the confidence interval

= where

0.95

We were asked to make a bootstrap of our samples. A bootstrap population is derived from a sample population. We take an average of the random sample from a population and add that to our bootstrap population. We repeat this many times with different sample populations. We can use this information to make assumptions of our sampling population. Here is an example of a bootstrap population taken from our sample population of students. This is based on the amound out hours students spent playing video games.

nmatheson — Tue, 19 May 2009 21:17:09 +0000

Here we will try to show that the expected value of the sample average is the population paramter ie pop. average.

from this we can calculate the population variance and standard deviation

If is known then the sample size can be chosen to give an acceptable level of accuracy in the estimation.

nmatheson — Tue, 19 May 2009 20:26:09 +0000

Students were asked if they played video games the previous week. They also had a test the following week. this information can help us make an assumption on the quality of information received. Here is a histogram of the hours the student played video games the week prior.

As you can tell most students did not play video games.

nmatheson — Tue, 19 May 2009 19:04:50 +0000

In this Chapter we review a survey taken of students in an introductory statistics course. A total of 314 students participated in the course. The survey used 91 of the 314 students to analyze the results and make a prediction of students who played video games and the correlation on what their expected grade would be in the course.

The information asked was as follows:

Description :
time Time spent playing video games in week prior to survey in hours.

like Like to play video games
1=Never played, 2=Very much, 3=Somewhat, 4=Not really, 5=Not at all

where Where play video games
1=Arcade, 2=Home on a system, 3=Home on a computer 4=Home on computer and system, 5=Arcade and Home(system or computer) 6=Arcade and home (both system and computer)

freq How often play video games
1=Daily, 2=Weekly, 3=Monthly, 4=Semesterly

busy Play if busy
0=no, 1=yes

educ Is playing video games educational?
0=no, 1=yes

sex Sex
0=female, 1=male

age Age in years

home Computer at home
0=no, 1=yes

math Hate math
0=no, 1=yes

work Hours worked for pay in the week prior to survey

own Own PC
0=no, 1=yes

cdrom Owned PC has a CDROM
0=no, 1=yes

email HAve email account
0=no, 1=yes

grade Grade expect in course
4=A, 3=B, 2=C, 1=D, 0=F

nmatheson — Tue, 19 May 2009 18:43:13 +0000

Skewness and Kurtosis

skewness =

kurtosis =

skewness value for mothers who did not smoke
= -0.1869841

skewness value for mothers who did smoke
= -0.03359498

kurtosis value for mothers who did not smoke.
= 4.03706

kurtosis value for mothers who did smoke
= 2.988032

for the normal the kurtosis should be 3 and the skewness should be 0. As you can tell mothers who smoked have a very close value of both kurtosis and skewness to the normal.

We can use this to tell percentages based on the 68-95-99.7 rule.

Based on these observations we can derive that although the babies of mothers who smoked had a lower mean weight. The skewness of the distribution of weights compared to babies whose mother did not smoke affected it’s outcome.