Linear Associations – Concept and Explanation

Key Concepts

1. Linear Association

2. Strength of Linear Association

3. Recognise Non Linear Association

1. Recognise different patterns of scatter plots 

2. Recognise different types of correlation 

3. Recall what is a slope of a line  

Slope of a line measures the steepness and direction of line.  

slope = rise/ run 

Rise is the vertical change between two points, where as run is the horizontal change  between two points. 

4. Recall different methods to find the slope of a line , slope-intercept formula, two point formula  

• Slope is constant through out the line . 

• The slope – intercept formula for a line is y= mx + b, where m is the slope of the line and b is the y-intercept of the line. 
• If (x₁, y₁) and (x₂, y₂) are any two points on a line then slope of a line 

is (y₂ – y₁)/(x₂ – x₁). 

m = (y₂ – y₁)/(x₂ – x₁) 

slope of a horizontal line is zero and slope of a vertical line is not defined. 

1. If the rise is 20 units and run is 10 units then the slope of the line is——– 

2. Y= 2x + 1 is an equation of a straight line then the slope of the line is——— 

Line of best fit 

Line of best fit is a line through a scatter plot of data points that best expresses the relationship between those points. 

Linear Association 

When a straight line describes the relation between two variables then it is a linear Association. 

Example 1: 

Georgia and her classmates are measuring their height and arm span. They record their data in a table. 

How can they determine what relationship, if any, exists between the two sets of measurements? 

Step 1: Plot the data points in a scatter plot. 

Step 2: Use a pencil to find a line that passes through the middle of the plotted points. This line is called a trend line. 

Step 3: Look at the slope of the line. The slope is positive. 

Georgia can draw a trend line on the scatter plot to determine that there is a positive relationship between height and arm span. 

Perfect Linear Association 

Relationship between two variables is a perfect linear relationship, then a scatterplot of the points will fall on a straight line. 

Strong Linear Association 

The more the points tend to fall along a straight line the stronger the linear relationship.  

When the slope is 1 there occurs a strong linear association. 

Weak Linear Association 

A weak positive correlation would indicate that while both variables tend to go up in response to one another, the relationship is not very strong. 

Non Linear Association 

A nonlinear relationship is a type of relationship between two entities in which change in one entity does not correspond with constant change in the other entity.  

An association between two variables in which the direction and rate of change fluctuate.  

Analysing Linear Association 

The easy way to interpret a linear association is using slope-intercept formula y=m x + c , where   
m is the slope of the line and c is the y intercept. 

Scatter plots can show a linear association, a nonlinear association, or no association. For scatter plots that suggest  a linear association, you can draw a trend line to show the association. You can assess the strength of the association by looking at the distances of plotted points from the trend line.

Exercise:

1. What is line of best?

2. What is linear association?

3. How do you analyse a linear association?

4. What is Perfect linear association?

5. What is the slope of strong linear association?

6. Draw a graph giving non linear association?

7. What is the slope of horizonatal line?

8. What is the slope of vertical line?