Linear regression analyzes the relationship between two variables, where one variable (X) is considered to predict or cause changes in the other variable (Y). It fits a straight line through the data points on a scatterplot to represent the trend of Y values as X changes. The regression line shows the average relationship between X and Y, allowing Y values to be estimated based on X. Higher correlation values (closer to 1 or -1) indicate stronger linear relationships between the variables.

1. Linear Regression

2. Linear Regression
 Involves two variables that are paired
because there is a relationship between
them
 Deal with measurements made on two
variables X and Y - bivariate
 Ex. height and weight, achievement &
learning approach, study habits &
grades, achievement and aptitude

3. Linear Regression
 There is a straight line relationship
between variables X and Y
 When X increases, Y also increases-
positive relationship
 When X increases, Y decreases or vice
versa – negative relationship

4. Relationship between achievement and
aptitude
Achievement (X) Aptitude (Y)
100 99
95 98
90 94
85 87
82 84
80 81
75 78
70 73
65 68
50 60

5. Regression Line between achievement and
aptitude
Scatterplot: X v s. Y
Y = 14.379 + .85633 * X
Correlation: r = .98966
105
100
95
90
85
80
Y
75
70
65
60
55
40 50 60 70 80 90 100 110
X 95% conf idence

6. Laziness Perseverance
100 35
95 40
90 45
85 50
75 55
70 60
65 64
60 70
55 76
50 80

7. Relationship between Laziness and
Perseverance
Scatterplot: Y v s. X
X = 139.94 - 1.138 * Y
Correlation: r = -.9959
110
100
90
80
X
70
60
50
40
30 40 50 60 70 80 90
Y 95% conf idence

8. Y can be predicted based on
the value of X
 Y = a + bX