Correlation and Regression
[Pages:54]Correlation and Regression
Tsitsi Bandason BRTI
12th March 2019
Objective of the Session
? To find relationships between quantitative variables and testing the validity of the relationship
Introduction
? Statistical analysis is a tool for processing and analysing data and drawing inferences and conclusions
? It is also a double edged tool easily lending itself to abuse and misuse
? Abuse can occur when poor data is collected and sophisticated techniques used resulting in unreliable result
? Misuse can occur when good data is collected and poor techniques are used resulting in poor results
? Misuse can occur when good data is collected and good techniques are used but there is poor interpretation of results
Correlation
? Correlation is a bi-variate analysis that measures the strength and direction of relationship between two quantitative variables
? High Correlation means Strong relationship ? Direction of the relationship is indicated by the
sign of the coefficient: + sign mean a positive relationship and a ? sign means a negative relationship
Types of Correlation
? Pearson's coefficient of correlation (r) for symmetric, bell shaped data - for normally distributed variables
? Spearman rank correlation is correlation between ranks - for ordinal or skewed data (non-parametric)
? Kendal's tau is appropriate - for ordinal or skewed data with ties and/or with small sample (nonparametric)
Questions Answered by Pearson's Correlation
? Is there a statistically significant relationship between age, as measured in years, and bone density, measured in mg/m2 ?
? Assumption
? Variables are Normally distributed ? There is a linear relationship between them. ? The null hypothesis is that there is no relationship
between them
Pearson Correlation Interpretation
? Measures strength of linear relationship ? r lies between -1 and 1
? If r = -1 there is perfect negative linear relationship
? If r= 0 there is no linear relationship ? If r=1 there is perfect positive linear relationship
? Can test whether a correlation coefficient r is statistically significant using a t-test
Scatter Plot of Relationships
150 140 130 120 110 100 90 80 70 60 50
0
Perfect positive correlation
r=1
2
4
6
8
10
12
150
Perfect negative correlation
140
130
120
r=-1
110
100
90
80
70
60
50
0
2
4
6
8
10
12
170.0
Strong negative correlation
150.0
r=-ve
130.0
110.0
90.0
70.0
50.0
0
2
4
6
8
10 12
80
Quadratic function
75
70
65
60
55
50
0
2
4
6
8
10
12
150 140 130 120 110 100 90 80 70 60 50
0
Random values
r=0
2
4
6
8
10
12
150 140 130 120 110 100 90 80 70 60 50
0
No correlation
r=0
2
4
6
8
10
12
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