research skills 11 regression and correlation

Question 1

what does pearsons R tell us ?

Answer 1

• strength of correlation and the direction
• If the correlation is positive the number will be +ve - between +1 and 0
• If the correlation is negative the number will be –ve - between 0 and -1
• 0 represents no correlation.

Question 2

what is regression analysis ?

Answer 2

• Often, you have a dependent variable — the main factor that you’re trying to understand or predict.
• And then you have your independent variables — the factors you suspect have an impact on your dependent variable.
• Regression analysis is a way of mathematically sorting out which of those variables does indeed have an impact.

Question 3

what is the regression equation ?

Answer 3

• representing how much y changes with any given change of x can be used to construct a regression line on a scatter diagram.
• The direction in which the line slopes depends on whether the correlation is positive or negative.

The two features of the line that we must know are:
the distance above the baseline
the second is its slope.

• They are expressed in the following regression equation : ŷ = ax+b
  a = slope
  b= intercept
  y and x = graph coordinates

Question 4

what is interpolation and extrapolation ?

Answer 4

You can predict the value of a variable by reading it off the graph.

If your unknown falls within the range of the graph (your standards) then this is called interpolation.

If the unknown sample falls outside the range of the graph then this is called extrapolation.

Question 5

how do we find out how well the regression line fits the data ?

Answer 5

This measure is given by the r squared (r2) – between 0 and 1. (1 is perfect)

The r squared is closely related to the Pearson’s r – it is just the Pearson’s r value squared.

However – Pearson’s r tells you about the direction of the relationship between the 2 variables e.g. whether it is positive or negative.

R squared only tells the measure of the amount of variance in your dependent variable (y) that is explained by your independent variable x.

Question 6

how can you find values of your unknown against standard curve ?

Answer 6

• find regression equation
• rearrange equation if you want to find x
  plug in numbers