maths unit 3
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what is univariate data
the study of only one variable
what is bivariate data
the study of two variables at the same time to determine if there is a relationship that exists between them + how this relationship can be used to make predictions
what do you talk about when describing relationships in scatterplots
• the form - is it linear or non-linear • the direction - is it positive or negative • the strength - strong, moderate, weak • possible outliers
what do dif letters mean in pearson’s correlation coefficient
n = no. pieces of data xi = x - value (explan) yi = y value (resp) sx = stan dev. x-values sy = stan dev. y - values - and then the means
what to put in pearson’s correlation coefficient table
• stuff in first set of brackets • stuff in second set of brackets • then multiply by each other
what form. for equation of a line
y = mx + c m = gradient (y2-y1/ x2-x1) c = y-int
least squares regression line form.
y = a + bx y = response variable x = explanatory b = gradient of the line (r x sy/sx) (r = corel. coefficient)
what to do in least squares reg line when explanatory variable is equal to 0
value of response variale is indicated by the y - intercept
what are residual values and how you find them
length of vertical line joing data point to regression line = actual y value - pred. y value
what seasonal trend
data fluctuates according to the calendar
what cyclical trend
fluctuations repeat due to reasons other than the calendar
what irregular trend
no obvious pattern
what is an arithmetic sequence
the dif. between any two successive terms
whats the common dif, how do you find (arithmetic sequences)
d = tn+1 - tn e.g. t2 - t1, t3 - t2, etc
how to make predictions using arithmetic sequence rule
tn = t1 + (n-1)d
recurrence relation for a simple interest loan/ investment?
Vo = a, Vn+1 = Vn + d Vo = initial amount d = interest added each year
recurrence relation for straight-line depreciation?
Vo = a, Vn + 1 = Vn - d Vn = value of asses after n years d = depreciation amount each year
how to find future value of an asset with depreciation rule?
Vn = Vo - nd Vn = future value Vo = initial value d = amount of depreciation each year
rule for when assets depreciate based on usage rather than age?
Vo = a, Vn + 1= Vn - d Vn = value of asset after n outputs d = depreciation amounts per output
how are geometric sequence terms found?
multiplying each term by r (common ratio) - to find this: t2/t1, t3/t2, etc
recursive def. of a geometric sequence?
t1 = a, tn + 1 = tn x r (common ratio)
general rule for geometric sequence?
tn = t1 x r ^n-1
recurrence relation for reducing balance depreciation
Vo = purchase price, Vn + 1 = Vn x (1-i) i = depreciation rate Vn = value of asset after n depreciating periods
how to find the future value of an asset due to reducing value depreciation
Vn = Vo (1 - i) ^n Vn = future value Vo = purchase price