Math 151 , Fall 2005,  Day 24 Friday Oct. 21 Hit reload ...  After class

Exam 2 Monday (Day 25, Oct.24).  Covers parts II and  III . Sign up today if you need a special time to take the exam.
How much computational detail from part II?  You don't need to know the formula for the correlation coefficient, but you should be able to guess roughly the r from a scatterplot, and know and use the properties pp.121-2.You will need to know, among other things,  how to find b₀ and b₁ from the means, standard deviations, and r of the x-and y-values,  and to give the formula for the regression line, (like 17, p.154); and to graph the regression line on top of the scatterplot.  Also find by hand the value that the line predicts for a particular x.  You should be able to identify and calculate the residual value for a particular x-y point as its vertical distance from the line (negative if the point is below the line), and identify and understand potential influential points.  You should know  that the regression line goes through the point given by the two means, and that the  regression line "rises" r standard deviations in y for each standard deviation increase in x (pp. 137-8); also that the regression line of "weight" on "height" is not the same line as the regression line of "height" on "weight" . You should be able to describe verbally the meaning of R² in the context of a data set.

Day 24 (Friday Oct. 1 ): Prepare for Exam.
    Next, D&V Part IV: Ch. 14, Ch.15 thru p.  291 (then Ch. 18 &on.) ActivStats is very good for part IV--Ch11"Randomness" shows Law of Large Numbers as D&V express it. Ch14, 15"Intuitive Probability"&"Probability Rules" correspond well with the text and present very good examples.

Hand in Wednesday?? NO.  Friday probably = =  Finish reading Webpage Day 23, do these: ActivStats, Ch.11 HW, ACT 1 and ACT 2: (The disk in your book is fine for this; you don't need SPSS. ) In Ch. 11("Understanding Randomness") click on the "house" icon on the top menu bar to get the HomeWork.  Do problems ACT 1 and ACT2, using the "Randomness tool" which opens when you click on the button in the HW problem.  1 Roulette 3  Winter 6  Crash 9 Spinner 11 a Car repairs 13 a M&M's Using independence:  (text below) 11 b Car repairs 13 b M&M's 19 Champion bowler 15 Disjoint or indep?  Read p.290 top, with this.  Chapter 15, p. 299 1 Sample spaces

Read,   to  discuss    = = = = =  Chapter 14  (uses independence): Read p.283 #25,  read answers in back. (a) should have 0.001, not 0.00 for the answer.

Op- tion- al

Questions for exam?
Took whole class.  Start Part IV Wednesday
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Part IV: Randomness and Probability.  Day 23  .

Continuing from Day 23:
Flipping-coin-twice was built from a simpler phenomenon; flipping coin once: P(H) = .5, P(T) = .5

Rule 5.  If A and B are two independent events, the probability that both A and B occur  is the product of the probabilities of the two events.  P(A and B) = P(A)×P(B), if (and only if) A and B are independent.
   Rule 5 can be used to build probabilities for complex phenomena from simpler ones (Ch. 14); to check structure in existing sample space (Ch. 15.)

e.g. Pick 2 people at random from U.S. pop.  (Pop. is so big that it's hardly changed by removing first. Independence OK)
   P(First has 4+ yrs college, and 2nd didn't graduate HS) = .230×.183 = .042
   P(First didn't graduate HS, and 2nd has 4+ yrs college) = .183×.230 = .042
   P(one didn't graduate HS, and the other has 4+ yrs college) = .042+.042= .084

Highlights:

Sample Chosen from a  Population
  Numerical summary: Statistic (Latin)  Parameter(Greek letter)

The actual value of the Statistic will vary, depending on the particular sample. "Sampling variability" = "Sampling error"
The Statistic "estimates" the Parameter.   If we choose simple random samples, we can understand the pattern of values the statistic can take.

Chance ("Stochastic")  behavior (a random phenomenon): Unpredictable in the short run,  predictable regular pattern in the long run.
"Probability" of particular something happening: proportion of times it would happen in a very long series of independent repetitions (trials) of the phenomenon: "long-run relative frequency".
    (independence:  outcome of one trial must not influence the outcome of any other.)

Law of Large Numbers (LLN):  Relative frequency of repeated independent trials gets closer  to the "true" relative frequency as the number of trials increases. Aberrations won't be compensated for; they will only be swamped out.  (Misconception of "law of averages.")

A Random phenomenon,   Sample space S. ("Events")  Probability model: S, and a way of assigning a probability to each event.

Probability rules:  A an event in sample space S, P(A) is "the probability that  A occurs"
    These rules are all true for proportions in long run (Probabilities), prop.of counts, proportions of areas.
    1.  0 < P(A) < 1
    2. P(S) = 1
    3. For any event A, P(A does not occur) = 1 - P(A)
    4.  A and B are  disjoint if they have no outcomes in common (can't happen simultaneously.)
          If A and B are disjoint, their probabilities add:  P(A or B) = P(A) + P(B)
 5.  If A and B are two independent events, the probability that both A and B occur  is the product of the probabilities of the two events.  P(A and B) = P(A)×P(B), if (and only if) A and B are independent.