HTHSCI 2S03 Lecture Notes - Lecture 7: Test Statistic, Dimensionless Quantity, Statistical Hypothesis Testing
26 May 2018
School
Department
Course
Professor
2S03: Sessions 10 & 11
Correlation, Simple Linear Regression, Multiple Regression
Correlation and Simple Linear Regression
• It is frequently desirable to learn about the relationship between two variables.
• For example, we may be interested in studying the relationship between:
o blood pressure and age
o height and weight
o The con centration of an injected drug and heart rate
o The consumption of some nutrient and weight gain
o Total family income and medical care expenditure
• Regression and correlation techniques can be used to examine the nature and strength of the
relationship between two variables.
• Although these techniques are related, they serve different purposes.
Regression: we can describe it using an equation, only looking at relationships that make straight lines
Correlation: how strong are these variations related to one another?
Correlation Analysis- Introduction
• There are a number of correlation coefficients for different types of variables
• Toda e disuss Pearso’s, hih is used he oth ariales are normally distributed
(continuous) random variables
• Pearso’s easures the stregth of the linear relationship between two variables
The Correlation Model- Formula
• The correlation coefficient for a sample is denoted by r
• The sample correlation coefficient is r= -0.791. This is a point estimation of the population
correlation coefficient, rho (p).
• If r= 0, there is no correlation
Questions:
• Is this value of r statistically significant?
• What is the appropriate statistical test for p?
The Correlation Model -Some Specifications of Correlation Coefficient
• The correlation coefficient, either r or p, is a dimensionless number; it has no unit of
measurement
Correlation coefficient: -1 < 0< 1
• If p=1, there is a perfect direct linear correlation between the two variables
• If p=-1, there is a perfect inverse linear correlation between the two variables
• If p=0 ,there is a no linear correlation between the two variables.
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Lecture Question 1 (session 10)
If there is a very strong correlation between two variables then the correlation coefficient must be:
1. Any value larger than 1
2. *Much smaller than 0, if the correlation is negative
3. Much larger than 0, if the correlation is negative
4. Much larger than 0, regardless of whether the correlation is positive or negative
Ha: there is either a negative or negative relationship
H0: no relationship
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General Rules of Thumb for Strength of the Relationship
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