ESE633� Statistic in Education��Chapter 9�SIMPLE LINEAR REGRESSION� Video E� �

Dr Kim Teng Siang

kskim2007@gmail.com

0124661131

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INTRODUCTION

We want to find the relationship between IQ and

Mathematics Achievement (DV)

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IQ --> IV , interval scale

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Math Scores --> DV , interval scale

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How to find the relationship?

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Scatter plot

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Math Score = Y axis

IQ = X axis

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Scattergram

1. Plot of All (X_i, Y_i) Pairs (points)
2. Suggests how well which relationship Model (line) will fit

(Linear Model of relationship)

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Math

score

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IQ

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0

20

40

60

0

20

40

60

X

Y

Thinking Challenge

How would you draw a straight line through the points? How do you determine which line ‘fits best’? (balance for all points)

Math

Score

IQ

Thinking Challenge

How would you draw a line through the points? How do you determine which line ‘fits best’? (balance for all points)

Math

Score

IQ

Thinking Challenge

How would you draw a line through the points? How do you determine which line ‘fits best’?

Thinking Challenge

How would you draw a line through the points? How do you determine which line ‘fits best’? (balance for all points)

Thinking Challenge

How would you draw a line through the points? How do you determine which line ‘fits best’? (balance for all points)

Thinking Challenge

How would you draw a line through the points? How do you determine which line ‘fits best’? (balance for all points)

Math

Score

IQ

Other Non-linear Relationships

No Relationship

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0

20

40

60

0

20

40

60

X

Y

Scattergram

Non-linear Relationship - Curve

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0

20

40

60

0

20

40

60

X

Y

Types of �Regression Models

Regression

Models

Linear

Non-

Linear

2+ Explanatory

Variables

Simple

Multiple

Linear

1 Explanatory

Variable

Non-

Linear

Linear Equations

High School Teacher

© 1984-1994 T/Maker Co.

Linear Regression Model �for Prediction

Relationship Between Variables is in a Linear Function

Y

X

i

i

i

=

+

+

β

β

ε

0

1

Dependent Variable (Response) �(e.g., income)

Independent Variable (Explanatory) �(e.g., education level)

Population Slope

Population �Y-Intercept

Random Error

Inference About the Population Slope and Intercept

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• If then we have a graph like this:

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X

Inference About the Population Slope and Intercept

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• If then we have a graph like this:

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X

This is the mean of Y for those whose independent variable is X

Inference About the Population Slope and Intercept

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• If then we have a graph like this:

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X

Note how the mean of Y does not depend on X: Y and X are independent

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*

*

*

*

*

*

*

*

*

English

score

Attitude

Scatter plot shows that there

Is a linear relationship between

English score (DV) and

attitude (IV)

Estimating Regression

Coefficients Using SPSS

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Based on data in Table 9.1,

page 4

Estimating Regression Coefficients Using SPSS

• Refer to page 4
• (Type in the values in Table 9.1)
• Lets carry out the Testing procedure using Linear Model
• a) Test for Linearity (Global Hypothesis)
• R² = 0
• b) Test of Sig. of Slope

- Regression slope is equal to zero

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a) Testing the Assumption of Linearity (Global Hypothesis)

• Ho: The variation in the DV is not explained by the Linear Model (R² =0)

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• H1: A significant porting of the variation in the DV is explained by the Linear Model (R² = 0)

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Is there a Linear Regression (Table 2 & 3)?

Predictors: (Cons tant), ATTITUDE

Table 2 : Model Summary

Table 3 : ANOVA

R square = .88, and ANOVA shows that it is significantly not zero

Conclusion: there is a Linear relationship betw English score and attitude

b) Testing the Significant of the Slope

• Ho : The regression slope is equal to

zero (beta = 0)

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• H1: The regression slope is not equal to

zero (beta ≠ 0)

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‘Coefficients’ table (see Table 4).� 

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Significant

Beta 1 or slope is not zero

Predicting English Performance

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ENGLISH Score (Y) = β1X +  βo

= Slope ((β1) multiplied by Attitude Score (X)) + Intercept (βo)

REGRESSION EQUATION

• The simbol ‘β’ is pronounced as “beta”

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• So β0  is pronounced ‘beta zero’ which is the intercept

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• and β1 is pronounced ‘beta one’ which is the slope

 (Should be reverse: Beta 1 is the slope, beta zero is the

constant or intercept)

To Predict performance when attitude score is 30.0

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• ENGLISH performance (Y) = 1.50 X 30.0 + 0.70

= 45.70

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• By applying the regression equation, the predicted score is 45.70.

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Assignment Question 2

• Explain the Relationship between 2 variables (interval scale),
• Statistical test used

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Reading

Comprehension

Hours spent playing video games

Thank You

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