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2 ;"CORRELATION AND REGRESSION"
2 ;"CHI-SQUARED"
2 ;"BINOMIAL DISTRIBUTION"
2 ;" ";
2 '" 1 HHH + 3 HHT + 3 HTT + 1 TTT."
2 - an explanation"
1 yy=(ff+rb*q)*fa+26
1 y$="1/(sz*2.506)*
1 y valuesI
1 xf=xf*(x-y):
1 v=(a(j)-g)*ra+25
1 the value found (x),
1 the value expected (y),"'"
1 the binomial probabilities:
1 ss=ss+a(j)^2
1 sf=sf+b(j)
1 s=s+a(j)*b(j)
1 s9=s9+dx*dx
1 s8=s8+dx*b(k)
1 s7=s7+dx*dy
1 s1=s1+a(j)
1 regression
1 of getting at least 1 six are
1 ntf=ntf*(nt-x-w):
1 nf=nf*(nt-z):
1 nearly 1 in 2
1 ne*s0*s2=0
1 ff=my-mx*rb
1 f=(b(j)-lf)*fa+27
1 eg 10 in this case."
1 dy=b(k)-my
1 dx=a(k)-mx
1 d(j)=p^(nt-j+1
1 correlation
1 chi=chi+(a(j)-b(j))*(a(j)-b(j))/b(j)
1 cc=cc+c(x+1
1 c(j)=c(j)*d(j)
1 b(j)=c(j):
1 b$="y values"
1 and"''" -
1 add in appropriate details
1 ^-mp)*(mp^x)/xf
1 Scatter diagram"'"
1 STATISTICS\
1 Poisson distribution
1 PART 3 YU
1 PART 2
1 Inspect normal curve
1 Graph data
1 GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBV@GGGGGGGGGGGGGGGGGGGGGGGGGGGGBVt@GGGGGGGGGGGGGGGGGGGGGGGGGGGBVte@GGGGGGGGGGGGGGGGGGGGGGGGGGBVtehGGGGGGGGGGGGGGGGGGGGGGGGGGBVtehGGGGGGGGGGGGGGGGGGGGGGGGGGBVtehGGGGGGGGGGGGGGGGGGGGGGGGGGBVtehGGGGGGGGGGGGGGGGGGGGGGGGGGBVtehGGGGGGGGGGGGGGGGGGGGGGGGGGBVtehGGGGGGGGGGGGGGGGGGGGGGGGGGBVtehGGGGGGGGGGGGGGGGGGGGGGGGGGBVtehGGGGGGGGGGGGGGGGGGGGGGGGGGBVtehGGGGGGGGGGGGGGGGGGGGGGGGGGBVtehGGGGGGGGGG
1 Correlation and regression
1 Chi-squared
1 Binomial distribution
1 ;z$;" Entry ";j;"; enter y value"
1 ;z$;" Entry ";j;"; enter x value"
1 ;g;" x values"
1 ;"weight increases"
1 ;"published chi tables."'
1 ;"not strongly supported."
1 ;"mpg decreases"
1 ;"experimental values";
1 ;"as speed increases,";
1 ;"as height increases,";
1 ;"and chi>6, the theory is";
1 ;"____________"
1 ;"________"
1 ;"_______"
1 ;"_ _ _ _ _ _";
1 ;"_ + _ + _ + _ = 1";
1 ;"_ _ _ _"'" 8 8 8 8"
1 ;"_ + _ + _ = 1"'" 4 2 4"
1 ;"With 15 or fewer";
1 ;"T";j;"=";
1 ;"Std dev= ";sd
1 ;"Std dev = ";sz
1 ;"Sorry - maximum of 25 permitted":
1 ;"Select mode from 1 to 11 and press ENTER."
1 ;"SCATTER DIAGRAM"
1 ;"Relationship";
1 ;"Regression equation is:"
1 ;"R value";
1 ;"Press: C-calculate probability; M-more throws; P-plot binomial dist'n"+("; other letter-continue"
1 ;"Press: C - correlation value; any other letter - new mode."
1 ;"Press: C - compare with normal; any other letter - change mode"
1 ;"Press: C - compare with normal; any other letter- results"
1 ;"Press: C - chi-squared test; any other letter - new mode."
1 ;"Press: C - calculation; any other letter - new mode."
1 ;"Press: A - another normal curve;any other letter - new mode."
1 ;"Press any letter to continue."
1 ;"Press S for sound;"'" any other letter for silence!"
1 ;"Please refer to";
1 ;"POISSON DISTRIBUTION"
1 ;"No interaction";
1 ;"Mean= ";mn
1 ;"Mean = ";nm
1 ;"Inverse but partial";
1 ;"Inverse and full"
1 ;"INSPECT NORMAL CURVE"
1 ;"How many entries? "
1 ;"GRAPH DATA "
1 ;"GENERAL STATISTICAL PROGRAM"
1 ;"Examples";
1 ;"Error; not in your stated range"
1 ;"Error - whole number required.":
1 ;"Error - whole number required. ":
1 ;"Error - Positive value required":
1 ;"Enter smallest value of x":
1 ;"Do you want sound?"
1 ;"Direct but partial"
1 ;"Direct and full";
1 ;"Corr. coeff. R = ";(
1 ;"Computer calculating!"
1 ;"Chi = ";chi
1 ;"= 1-125";
1 ;"8 8 8 8"
1 ;"6"'''" ie,
1 ;"2 2 2 2 2 2"
1 ;"1 3 3 1";
1 ;"0 x values"
1 ;"...Height/weight:";
1 ;"...Car speed/mpg:";
1 ;" to appear about one-sixth of the total number of throws."
1 ;" Number of events must be positive; please re-enter.":
1 ;" Error - probability required between 0 and 1":
1 ;" 2 xy"''
1 ;" 1*1*1 + 2*1*1 + 1*1*1";
1 ;" _ _ _ _ _ _"'" 6 6 6 6 6 6"
1 ;" 1 1 1";
1 ;" SELECT MODE "
1 1^-((x-nm)*(x-nm)/(2*sz*sz))C
1 1^-((x-nm)*(x-nm)/(2*sz*sz))"
1 1/(sz*2.506)*
1 /(ne*s0*s2)+.5
1 /(h-g))*100
1 /(h+(s$="S")-g)
1 ,tc;"Term ";x+1
1 *q + 3*p*q
1 *5+3*1*(5)
1 )=nf/(xf*ntf):
1 );"=";nf/(xf*ntf)
1 (v0/sf)+.5
1 (v0/sf)*100
1 (sd/mn*nm*100
1 (b(k)-my)^2
1 (a(k)-s/sf)
1 (a(k)-mx)^2
1 ((s/sf)*100
1 ((mn-g)*(10
1 '''" Two techniques used as aids in deciding whether a"'" relationship exists between"'" two different variable"'" samples are:"
1 ''" b stands for the binomial"'" coefficients which depend on n."
1 ''" The program can run in silence."
1 ''" The likely outcome of tossing a coin several times can be calculated algebraically."
1 ''" The correlation coefficient
1 ''" The chances of throwing 5 sixes in 5 throws are given by the formula:"'
1 ''" The Poisson probability for ";x;" events is:"
1 ''" So, in 3 throws, the chances
1 ''" R varies in value between"'" 1 and -1."
1 ''" Press: S - single values"''" C - classed data"
1 ''" Please refer to published"'" statistical tables for the"'" significance of the result."
1 ''" For both, 4 (1+2+1) outcomes are possible."
1 ''" Comparing these two, you can see parallels:"'
1 ''" Welcome to this program."
1 ''" 1 HH 1 x
1 ''" (x+y)
1 '" the computer will calculate the chi-squared value for this data."
1 '" q is the probability of ""failure"" (eg not getting"'" a head)"
1 '" p is the probability of ""success"" (eg getting a head)"
1 '" p = 1 * (1)
1 '" ie, the result is:"'
1 '" Variance:";
1 '" Tossing a coin twice has four possible results:"
1 '" This is the equation of the"'" straight line which, when"'" drawn through the data in a scatter diagram, approximates best to the general pattern of change of the variables."
1 '" This gives:"'
1 '" The sum of the probabilities of these results is 1, ie:"
1 '" The probability of getting HHH is 1 in 8; that of HHT, 3 in 8."
1 '" The general formula where the number of ""throws"" is 3 is:"
1 '" The chances of getting at"'" least 1 six in 3 throws are given by the calculation:"
1 '" The chance of throwing a six is 1 in 6 (p=1/6)."
1 '" The chance of not throwing a six, q, is 1-p, ie q=5/6."
1 '" Suppose you throw a ""true"" die a large number of times. You would expect each value (eg 6)"
1 '" Sum of squares:";
1 '" Sum of deviations:";
1 '" Standard deviation:";
1 '" So the probability of getting 3 sixes in 3 throws (n=3) is:"
1 '" So in 60 throws you should get 10 sixes, 10 ones and so on."
1 '" Sample variance:";
1 '" Sample std. dev.:";
1 '" Repeating this process yields the same parallels:";
1 '" PROBABILITY is an estimate of the number of times a specific result is likely to occur."
1 '" Number of items:";
1 '" Mean:";
1 '" Incidentally, q = 1-p."
1 '" If you toss it twice, the"'" results possible are:";
1 '" If you toss a coin once, the chance of a head is 1 in 2, and that of a tail 1 in 2."
1 '" If you toss a coin 3 times, the result is 1 of 8 possible"'" combinations:";
1 '" If you square the 2-term"'" (BI-nomial) expression (x+y)"'" you get:"
1 '" If you input these pairs of values, ie:"
1 '" If you give H and T the value 1/2 each and treat the above line as an equation, you get:"
1 '" If the number of throws is 3, the probabilities are:"
1 '" How many throws (trials)?":
1 '" Here p and q have replaced H and T."
1 '" For n chance events, the"'" general formula for the"'" binomial probability of any combination of results is:"
1 '" For each possible result, you will have:"
1 '" Error - largest must be bigger than smallest!":
1 '" Enter trial mean ";
1 '" Enter smallest value of y":
1 '" Enter number of events ";
1 '" Enter largest value of y":
1 '" Enter largest value of x":
1 '" Do you want the computer to"'" carry out a correlation and regression calculation for"'" you?"
1 '" As an example of the formula, suppose you throw a die."
1 '" 1 + 3 + 3 + 1 = 1";
1 '" - x, the value found"''" - y, the value expected,"
1 '" - ring when input is required"''" - buzz if you make a mistake"''" - beep each key depression."
1 '" 4 8 16"'" possible combinations"
1 '" 2 3 4 times"
1 '" 1 HH + 2 HT + 1 TT."
1 '" 1 HH (both heads)"'" 2 HT (one head, one tail)"'" 1 TT (both tails)"
1 '"
1 "''" 2 HT 2 xy"''" 1 TT 1 y
1 " However, the computer can:"
1 " Enter probability p"
1 ROBIN ALLOTT, 1983"
1 LINEAR REGRESSION EQUATION
1 CORRELATION
1 BINOMIAL COEFFICIENTS
1 1 in 7776
1 - an explanation"'"
1 + 2xy + y
1 + ... + 1*q
1 eg 8"''" -
1 is a measure of how far one variable interacts with"'" another."
1 - calculation"'"
1 - calculation"'"
1 - calculation"
1 B