maths unit 3 Flashcards

1
Q

what is univariate data

A

the study of only one variable

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2
Q

what is bivariate data

A

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

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3
Q

what do you talk about when describing relationships in scatterplots

A
  1. the form - is it linear or non-linear
  2. the direction - is it positive or negative
  3. the strength - strong, moderate, weak
  4. possible outliers
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4
Q

what do dif letters mean in pearson’s correlation coefficient

A

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

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5
Q

what to put in pearson’s correlation coefficient table

A
  • stuff in first set of brackets
  • stuff in second set of brackets
  • then multiply by each other
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6
Q

what form. for equation of a line

A

y = mx + c
m = gradient (y2-y1/ x2-x1)
c = y-int

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7
Q

least squares regression line form.

A

y = a + bx
y = response variable
x = explanatory
b = gradient of the line (r x sy/sx) (r = corel. coefficient)

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8
Q

what to do in least squares reg line when explanatory variable is equal to 0

A

value of response variale is indicated by the y - intercept

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9
Q

what are residual values and how you find them

A

length of vertical line joing data point to regression line
= actual y value - pred. y value

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10
Q

what seasonal trend

A

data fluctuates according to the calendar

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11
Q

what cyclical trend

A

fluctuations repeat due to reasons other than the calendar

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12
Q

what irregular trend

A

no obvious pattern

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13
Q

what is an arithmetic sequence

A

the dif. between any two successive terms

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14
Q

whats the common dif, how do you find (arithmetic sequences)

A

d = tn+1 - tn

e.g.
t2 - t1, t3 - t2, etc

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15
Q

how to make predictions using arithmetic sequence rule

A

tn = t1 + (n-1)d

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16
Q

recurrence relation for a simple interest loan/ investment?

A

Vo = a, Vn+1 = Vn + d

Vo = initial amount
d = interest added each year

17
Q

recurrence relation for straight-line depreciation?

A

Vo = a, Vn + 1 = Vn - d

Vn = value of asses after n years
d = depreciation amount each year

18
Q

how to find future value of an asset with depreciation rule?

A

Vn = Vo - nd

Vn = future value
Vo = initial value
d = amount of depreciation each year

19
Q

rule for when assets depreciate based on usage rather than age?

A

Vo = a, Vn + 1= Vn - d

Vn = value of asset after n outputs
d = depreciation amounts per output

20
Q

how are geometric sequence terms found?

A

multiplying each term by r (common ratio)
- to find this:
t2/t1, t3/t2, etc

21
Q

recursive def. of a geometric sequence?

A

t1 = a, tn + 1 = tn x r (common ratio)

22
Q

general rule for geometric sequence?

A

tn = t1 x r ^n-1

23
Q

recurrence relation for reducing balance depreciation

A

Vo = purchase price,
Vn + 1 = Vn x (1-i)
i = depreciation rate
Vn = value of asset after n depreciating periods

24
Q

how to find the future value of an asset due to reducing value depreciation

A

Vn = Vo (1 - i) ^n

Vn = future value
Vo = purchase price

25
Q

what degrees are the north and south poles

A

90 degrees (N or S)

26
Q

what are great circles

A
  • the equator
  • all lines of longitude (not lat)
27
Q

where are tropic of cancer and capricorn

A

cancer - above equator (northern hem)

capricorn - under equator (southern hem)

28
Q

how are locations stated

A

LAT (N or S), LONG. (E or W)

29
Q

what is radius of the Earth

A

approx. 6371km

30
Q

how many km is 1 degree

A

11.2km

31
Q

how to calc. distance in km between two places on same great circle

A

D = 11.2 angular distance (N/S)

32
Q

how to calc. distance between km in small circles

A

D = 111.2cos0 x angular distance

0 = degrees of latitude
small circles have cos0 (cause radius has it in it)

33
Q

what are ahead/behind GMT

A
  • all places East Greenwich are ahead
  • all places West Greenwich are behind
34
Q

calc.ing time difference

A

24 hrs = 360 degrees longitude
1 hr = 15 degrees long
4 min = 1 degree long

35
Q
A