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CHAPTER 5 CORRELATION AND REGRESSION

Introduction Correlation and Regression Scatter Plot/Diagram Coefficient of Correlation Simple Linear Regression sanizah@tmsk.uitm.edu.my

Learning objectives

• Explain the concept of correlation • Calculate Pearson’s correlation coefficient and interpret the results • Calculate Spearman’s rank correlation for qualitative and quantitative data and interpret the results • Determine the regression equation for a set of data and interpret the equation • Use the regression equation to forecast

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Introduction

• Correlation: Do you have a relationship? (Between two quantitative variables, x & y) • If you have a relationship: ▫ 1) What is the direction? (+ or -) ▫ 2) What is the strength (r: -1 to +1) #Correlation measures LINEAR relationship. If you have a significant correlation: How well can you predict a subject’s y-score if you know their x-score?

Correlation & Regression

• Regression and correlation are two concepts used to describe the relationship between variables. ▫ Correlation is a statistical method used to determine if a relationship between variables exists. ▫ Regression is the statistical method used to describe the nature of the relationship between variables - that is, positive or negative, linear or nonlinear.

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Independent and Dependent Variable

• In this chapter, we want to study the relationship between 2 variables only. ▫ Independent variable – x ▫ Dependent variable - y • For example: ▫ Expenditure (x) and Revenue (y) ▫ Price (x) and sales (y) ▫ Number of days absent (x) and CGPA (y) ▫ Age of a person (x) and his/her blood pressure (y)

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Independent and Dependent Variable

Independent variable (x)

• Also called predictor or explanatory or manipulated variable • the variable in regression that can be controlled or manipulated

Dependent variable (y)

• Also called the response variable • the variable that cannot be controlled or manipulated

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Dependent(x) Vs. Independent(y)

• • • • Intentionally manipulated Controlled Vary at known rate Cause • • • • Intentionally left alone Measured Vary at unknown rate Effect

Example: What affects a student’s arrival to class?

Variables: • Type of School

▫ FSPPP, Business School, FSKM

• Type of Student

▫ Gender? CGPA?

• Class Time

▫ Morning, Afternoon, Evening

• Mode of Transportation

▫ Motorcycle, Car, UiTM bus

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QMT412 Pn. Sanizah's Notes

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Scatter Plot (scatter diagram)

• A scatter plot is used to show the relationship between two variables. • The scatter plot is a visual way to describe the nature of the relationship between the independent variable (x) and the dependent variable (y). • Interpreting scatter plots: ▫ ▫ ▫ ▫ Positive linear relationship Negative linear relationship Nonlinear relationship No relationship

Scatter Plot Examples

Linear relationships y y Nonlinear (Curvilinear) relationships

Positive

x y

x

y

x

Negative

x

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Scatter Plot Examples

Strong relationships y y

(continued)

Weak relationships

Scatter Plot Examples

No relationship y

(continued)

x y y

x y

x

x

x

x

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Example 1 (pg. 134)

x 1 3 5 7 9

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Correlation Coefficient

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• Draw a scatter diagram for the following data and state the type of relationship between the variables. 13 17

Correlation coefficient measures the strength and direction of a LINEAR relationship between a pair of random...