MATM FINALS: CORRELATION ANALYSIS Flashcards
- Measures the existence of relationship and association between two or more variables.
- to see the strength and the nature/direction of the relationship between two variables.
Correlation Analysis
it can be used to predict the changes that will happen on the other variable.
Other characteristics:
Stands alone
Stable
Unaffected by other variables
Usually expressed by the symbol “x”
Independent Variable
A variable where the values are expected to change as a result of changes in the values of the other variable (independent variable).
Other characteristics:
Observed or measured by the independent variable
Usually expressed by the symbol “y”
Dependent Variable
it is the diagram of the correlation analysis.
it is a type of plot or mathematical diagram using Cartesian Coordinates to display values for typically two variables for a set of data.
Scatter Plot
Two variables are positively correlated if the values of the two variables (both increase or both decrease.)
Two variables are negatively correlated if the values of (one variable increase while the values of the other decrease) and vice versa.
Two variables are not correlated, or they have zero correlation if (one variable neither increases nor decreases while the other increases or decreases.)
POSITIVE CORRELATION
NEGATIVE CORRELATION
NO CORRELATION
DEGREES OF CORRELATION
None (very scattered)
Low (scattered but visible that it is going one way)
High (bit scattered but more of a line)
Perfect (In a straight line)
TYPES OF CORRELATION
Positive - left going right up
Negative - right going left up
Curved - as is
Partial - left to right up but scattered at the top
Types of Linear Correlation
1. ______________ - shows DIRECT relationship between X and Y variables
ex. Income and Expenses
Income is the independent variable while Expense is the dependent variable.
Age and Weight
Age is the independent variable while Weight is the dependent variable.
- Positive Linear Correlation
- ____________________-
shows INVERSE relationship between X and Y variables
Examples: Which is the independent and dependent variable?
Academic Performance and Usage time of Cellphone
Usage time of cellphone is the independent variable while academic performance is the dependent variable.
Quantity of Food Servings and the Prices of Ingredients
Prices of Ingredients is the independent variable quantity of food servings is the dependent variable.
Negative Linear Correlation
a statistic showing the degree of relation between two variables
denoted by “r”
its value denotes the strength of association
its value ranges from -1.00 to 1.00
Coefficient of Correlation
+- 1.00
perfect correlation
+- 0.81 - 0.99
very high correlation
+- 0..71 - 0.80
high correlation
+-0.41 - 0.70
moderate correlation
+- 0.21 - 0.41
slight or low correlation
+- 0.01 - 0.20
negligible correlation
0
no correlation
Methods of Correlation
1. Pearson Product Moment Correlation or Pearson r (X.Y.XY.X2.Y2)
1st: multiply row x and y = xy
2nd: multiply x by itself = x2
3rd multiply y by itself = y2
4th: total each column
- formula is long
- Pearson Product Moment Correlation or Pearson r (X.Y.XY.X2.Y2)
r = [n(Σxy) − ΣxΣy]
_______________________________________
√[n(Σx2) − (Σx)2][n(Σy2) − (Σy)2]
Methods of Correlation
2. Spearman’s Rank Correlation Coefficient (“rs”) - r squared
YR (x) YR (y) Rank x Rank y D D2
1st: Rank the column YR (x) = Rank x
2nd: Rank the column YR (y) = Rank y
3rd: Rank x minus Rank y = D
4th: multiply D row to itself = D2
5th: total everything
- then the totalled no. you’re going to input in the formula and “n” is how many the rows are.
Spearman’s Rank Correlation Coefficient (“rs”)
6 ∑ 𝑑2 𝑟 = 1 − \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
𝑛 ( 𝑛 − 1 )
