BEES2041 Lecture Notes - Lecture 3: Simple Linear Regression, Linear Regression, Level Of Measurement
9 Jun 2018
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The method to solve the equation is to be careful of the errors that may occur during
calculation.
Regression
A simple linear regression decribes a functional (linear) relationship
Between a dependent variable (or response variable) and an independent variable (or
predictor variable)
Ratio data has a natural zero point e.g. Length of a caterpillar
Interval data: intervals between each value are equally split. E.g. Temperature
Ordinal refers to quantities that have a natural ordering(ranking) e.g. runners in a race
Linear correlation versus linear regression
-both are parametric methods for analysing relationships between variables
-they can be used on data measured on ratio, interval/ ordinal scale
-correlation is exploratory (are two variables significantly related?).. but there is no
expectation / prediction of cause
-The regression of one variable on another may suggest a hypothesis about why they are
functionally related
Examples on graphs:
Age of miss America & murders by steam, hot vapours & hot objects
Letters in winning words of scripps national spelling bee & number of people killed by
venomous spiders
Total US highway fatality rate & fresh lemon imported to USA from Mexico (Metric tons)
Be aware of lurking variables
=variable that is not among the explanatory / response variables in a study & yet may
influence the interpretation among those variables
Regression – not always casual
A significant regression relationship does not necessarily mean there is casual relationship
between the variables
e.g. child height vs uncalcified bone
additional growth dependent on, but not caused by the length of uncalcified bone in a six
year old childs finger
regressions can be useful in situations where it is impossible or expensive to measure the
response variable
one can measure the predictor(explanatory) variable instead
The mathematics of regression
Understanding the mathematical equations is important, in order to understand it , need to
be able to:
1understand computer output & interpret results
2understand limitations of techniques & appropriate usage
3redesign experiments to improve efficiency , overcome problems
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
The method to solve the equation is to be careful of the errors that may occur during calculation. A simple linear regression decribes a functional (linear) relationship. Between a dependent variable (or response variable) and an independent variable (or predictor variable) Ratio data has a natural zero point e. g. length of a caterpillar. Interval data: intervals between each value are equally split. Ordinal refers to quantities that have a natural ordering(ranking) e. g. runners in a race. Both are parametric methods for analysing relationships between variables. They can be used on data measured on ratio, interval/ ordinal scale. Correlation is exploratory (are two variables significantly related?) but there is no expectation / prediction of cause. The regression of one variable on another may suggest a hypothesis about why they are functionally related. Age of miss america & murders by steam, hot vapours & hot objects.
