102225 PPT- 4 STATISTICS COLLEGE.pptx Correlation: Perfect Positive Correlation

Correlation is a statistical measure that describes the strength and direction of a relationship between two variables.
Types of Correlation:

Positive Correlation – When one variable increases, the other also increases.
📈 Example: The more hours you study, the higher your test score.

Negative Correlation – When one variable increases, the other decreases.
📉 Example: The more you exercise, the lower your body weight.

Zero (No) Correlation – No relationship between the two variables.
⚪ Example: Shoe size and intelligence have no connection.
Symbol and Range:

Correlation is usually represented by r (the correlation coefficient).

r = +1 → Perfect positive correlation

r = –1 → Perfect negative correlation

r = 0 → No correlation

1. CORRELATION PREPARED BY: VIRGITA A. MANIPOL, LPT SOUTHERN PHIIPPINES INSTITUTE OF SCIENCE AND TECHNOLOGY

2. What is Correlation? Correlation is a statistical measure that describes the strength and direction of a relationship between two variables It tells us how one variable changes when another variable changes. Correlation does not imply causation-it only shows if variables are related, not whether one causes the other.

3. Types of Correlation 1 . Positive Correlation Both variables increases or decrease together. Example: Height and Weight - as height increases, weight tends to increase. 2. Negative Correlation One variable increases while the other decreases Example: Number of hours spent watching TV and exam scores-more TV time may be associated with lower scores

4. 3. No Correlation There is no apparent relationship between the variables Example: Shoe size and math grades – one does not affect the other.

5. Correlation Coefficient (r) A numerical measure of correlation is called the correlation coefficient (r) Range: - 1 to + 1 r = + 1: Perfect positive correlation r = - 1 : Perfect negative correlation r = 0 : No correlation

6. Example Using This Formula Suppose we have 3 students’ data: X (HOURS) Y (SCORES) XY X^2 Y^2 2 65 130 4 4225 4 75 300 16 5625 6 85 510 36 7225 ∑X = 12 ∑Y = 225 ∑XY = 940 ∑X^2 = 56 ∑Y^2 = 17075

7. Step 3: Interpret the result r=1 → Perfect positive correlation This means as hours studied increase, exam scores increase proportionally.

8. QUIZ-2

9. Question: The table below shows the number of hours students studied and their corresponding exam scores: NUMBER OF HOURS STUDIED EXAM SCORE 1 55 2 60 3 65 4 70 5 75

10. TASK: Determine whether there is a positive, negative, or no correlation. Explain your reasoning

11. 2. A survey collected the number of hours students spend watching TV per day and their average exam scores: HOURS WATCHING TV EXAM SCORE 1 90 2 85 3 80 4 75 5 70

12. TASK: Determine whether there is a positive, negative, or no correlation. Explain your reasoning