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.

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 relationships Positive : 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= 83.5 c) Moderate and positive f) About 95 thefts per day

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