A2 Stats Flashcards
describe exponential modelling
use logs & coding to convert exponential relationship to linear relationship & use regression line
y = ax^n –> logy = nlogx + loga & plot logx against logy
y=kb^x
logy = xlogb + logk & plot x against logy
define PMCC
product moment correlation coefficient
numerical measure of the type & strength of linear correlation
what is the PMCC for a sample & population represented by?
for sample: r
for population: ρ
what values is r b/w?
-1 ≤ r ≤ 1
r = 1 linear & positive correlation
r = -1 linear & negative correlation
r = 0 no correlation
what does n/a mean in table?
data for that day is not available
remove the points from calculations
describe how to find PMCC using calculator
menu –> 6: statistics
2: y = a + bx
enter values for x & y
option –> 4: regression calc
PMCC is r value
comment on suitability of a linear regression or exponential model for given data
e.g. as r is very close to 1, there is strong positive correlation b/w ___________. therefore the data points lie close to a straight line so a linear regression model is suitable for __________ data
so exponential model is suitable for raw data
what constitutes a ‘strong correlation’?
generally over 0.6 or less than -0.6
describe how to find equation of the regression line from coded data
‘unlog’
compare with the equation y = mx + c
logb =
loga =
work out a & b
state the equation at the end
what does significance level mean?
the chance of incorrectly rejecting H0 when it is true
what must the conclusion of a hypothesis test include?
accept/reject H0
RELATE TO CONTEXT OF THE Q
what is PMCC hypothesis testing used for?
used to determine whether the PMCC for a sample, r, indicates that there is likely to be a linear relationship within the population
what are the null & alternative hypotheses for PMCC hypothesis testing?
the H0 is always that there is no correlation in the population ρ = 0
for positive correlation ρ > 0
for negative correlation ρ < 0
for any correlation ρ ≠ 0 (NB halve the significance level)
describe the method of a PMCC hypothesis test
- state H0: ρ = 0
& H1 - significance level =
- n =
(n is number of pairs of data) - find critical value using the PMCC table in data booklet (one +ve & one -ve for 2-tailed test)
- do number line & if r value is outside critical region (see OneNote) then accept H0, but if r value is inside the critical region, reject H0
- conclusion
e.g. as 0.1149 (r-value) < 0.5067 (critical value), it is not in the critical region so we accept H0. there is not sufficient evidence of a positive correlation b/w daily maximum gust & relative humidity (linking to Q)
for any set notation Q, what is the first step?
draw Venn Diagram
dot method for P(A’ u B’) or P(A’ n B’)
for u: add things with at least 1 dot
for n: add things with all the dots
describe conditional probability
the probability of an event can change depending on the outcome of a previous event
the probability that event B occurs, GIVEN that event A has already occured
what is the notation for conditional probability?
P(B|A)
the probability that event B occurs, GIVEN that event A has already occured
usually P(B|A)…
≠ P(A|B)
in conditional probability, if A & B are independent, what is the formula?
P(B|A) = P(B|A’) = P(B)
two-way table
see OneNote & notes in folder
write down marginal totals
what is the addition formula?
given in FB
P(A u B) = P(A) + P(B) - P(A n B)
what is the multiplication formula?
not given in FB
P(B|A) = P(A n B) / P(A)
must divide by the probability of the 2nd letter
describe how conditional probabilities can be represented on a tree diagram
see Gordon OneNote
