5. Inter relationships between variables

Question 1

Inter relationships between variables

Answer 1

the strength and nature of the relationship between two sets of figures

Question 2

strength

Answer 2

correlation

Question 3

nature

Answer 3

Is it a straight line? is regression used to try and find the equation

Question 4

Correlation

Answer 4

2 variables are correlated if they are related to each other i.e. if the value of one changes does the other data set also change

can only ever be between +1 and -1

Question 5

Scatter diagrams

Answer 5

data points are plotted on a graph x axis independent variable (we choose it) y axis is dependant on the value of x

Question 6

regression

Answer 6

is what we use to work out the equation

Question 7

Perfect positive linear correlation

Answer 7

r = + 1

Question 8

Perfect negative linear correlation

Answer 8

r = - 1

Question 9

High Positive Correlation

Answer 9

r ≈ 0.9

Question 10

Moderate negative correlation

Answer 10

r ≈ -0.7

Question 11

No correlation

Answer 11

r ≈ 0

Question 12

Non linear or curvilinear

Answer 12

N/A

Question 13

Pearsons correlation coefficient

Answer 13

n = number of data points

FORMULA GIVEN IN EXAM

Question 14

Coefficient of determination

Answer 14

take correlation coefficient and square it

makes it easier to interpret the coefficient of correlation

tells us the proportion of changes in y that can be explained by the changes in x, assuming a linear relationship.

i.e. correlation coefficient is 0.7, correlation of determination is 0.49, meaning 49% if the changes in y are caused by the changes in x and that 51% relate to other factors

Question 15

Spurious correlation

Answer 15

where there is high value of correlation but no direct cause and effect

Question 16

Regression

Answer 16

where the regression line has the equation y = a +bx

find b using formula

then use formula to work out a

a = mean of y - bmean of x

Question 17

Interpolation

Answer 17

is when you estimate y when using a give value of x that is between the limits (outside the limit is extrapolation)

Question 18

Limitations of linear regression

Answer 18

just because we have a straight line doesn’t mean it is useful for forecasting

need to assume the relationship many not be linear

it could be spurious

need to be careful when using the regression line for extropolation

Question 19

Rank correlation: Spearman’s coefficient

Answer 19

when you want to calculate the correlation between two variables but one or both of them is not in a suitable quantitive form

i.e. student comes top in maths exam does that mean they will come top in econmics also, we interested in the rank not the absolute mark

d = difference in ranks

n = sample size