TWO VARIABLE ANALYSIS

By: Leslie Hamilton, Joseph Miller, Leah Brown, Racquel Thwaites, Ashlee Touzalin

Two variable analysis Definition: this involves the analysis of the

relationship between two variables

As one variable goes up, the other changes in a predictable way (either mostly goes up or mostly goes down)

Uses of two variable analysis

Science

Medicine

Educational research

Business

Geotechnology engineering - branch of civil engineering that focuses on earth, rock and subterranean water and their relation to planning, execution and operation of engineering projects.

INDEPENDENT AND DEPENDENT VARIABLE

Independent variable is a variable that stands alone and isn't changed by the other variables you are trying to measure.

Dependent variable is the variable that depends on other (independent variable) factors.

The value of the dependent variable depends on the value of the independent variable

Example The number days of your last hair cut and the

length of your hair

Independent:

Dependent:Days

Length

What is a Scatter Diagram

A scatter diagram is a tool for analyzing relationships between two variables.

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Time/ temperature scatter graph

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Identifying when and how to use

One variable is plotted on the horizontal axis and the other is plotted on the vertical axis

The pattern of their intersecting points can graphically show relationship patterns

Used to prove or disprove cause-and-effect relationships.

by itself it doesn’t prove that one variable causes the other

diagram can show that two variables are from a common cause that is unknown

When to use it To examine theories about cause-and-effect

relationships

to search for root causes of an identified problem

to design a control system

How to create a scattered diagram

Collect data

Draw the diagram

Label both axes

Plot the paired data

Title and label the diagram.�

Correlations Correlation is a measure of the strength of the

relationship or association between two variables

Positive Correlation For a generally upward shape in the points

plotted we say that the correlation is positive.

Independent variable the dependent variable

Negative Correlation For generally downward shape we say that the

correlation is negative.

independent variable the dependent variable

No Correlation For randomly scattered points with no upward or

downward tend, we say there is no correlation.

Types of relationshipsPositive : When the variable tend to have a

generally upwards shape

Negative: When the variable tend to have a generally downwards shape

Linear: When the variables seem to flow into a form of a line hence the word linear

Correlation strengths Strong: Which is when most of the variable are

closely together along the best line fit

Moderate: When the variables along the best fit, are slightly dispersed

Weak: when the variable is spread out unevenly, and most of the variables are not close to the best line fit.

Example Let's decide if studying longer will affect Regents

grades based upon a specific set of data.  Given the data below, a scatter plot has been prepared to represent the data. 

What is line of best fits A line of best fit is a line you draw through a

scatter graph to find the direction of an association between two variables.

How is it drawn “by eye”?Just an estimate

Therefore may look slightly different from others since not everyone sees the same way

How to find the equation of the line of best fits using coordinate geometry

Using the equation y = mx +c (there is no c in this example)

Use a point that is on the line of best fit for x and y

Or you could just find the gradient of the line

What we use the line of best fit to do?

The line of best fit is used to judge the two sets of data and determine their correlation.

To calculate values of one variable when given the other

What is interpolation and extrapolation?

Interpolating is using the values inside the poles

extrapolating is using the values outside the poles

these poles are created by using the lowest and highest value of x on the scatter diagram

it is unreliable to extrapolate outside the poles but reasonable to interpolate between them

Answer

Moderate, positive and linear

Answer

a) X= 6.88 Y= 83.5c) Moderate and positive f) About 95 thefts per day

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time/ temperature scatter graph

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Ashlee -Two variable Analysis and its uses / some of lines of best fits and correlations

Joseph - Independent and dependant

Leslie – Scatter graphs and correlations

Leah Lines of best fit

Racquel- Interpolation and extrapolation ( the two questions)

The End Hope you learned something