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Bjqp2013 - Statistical Technique for Decision Making

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BJQP 2013

STATISTICAL TECHNIQUE FOR DECISION MAKING

SEMESTER 1 2017/2018 (A171)

GROUP ASSIGNMENT

TITLE: CORRELATION AND REGRESION

PREPARED FOR: DR. HJ. MOHD AKHIR BIN HJ. AHMAD

PREPARED BY:

No.

Name

Matric Number

LOKE HUI TENG

253848

LIM QIAN QIAN

254724

KHNG ZHING-MEI

253614

CHUA KELLY

253912

HANG JIA SIN

253940

TAN YING LI

253847

                                                                     OBJECTIVE

The objectives of learning correlation and linear regression are:

  1. Understanding the uses of correlation analysis
  2. Calculate and interpret the correlation coefficient of the relationship between two variables, confidence and prediction.
  3. Apply the method of regression analysis and estimate the linear relationship between two variables.
  4. Evaluate the significance of the slope of the regression equation and the ability of regression equation to predict the standard estimate of the error and the coefficient of determination.
  5. Using log function to transform a nonlinear relationship to linear relationship.

TABLE CONTENT

NO.

CONTENT

PAGES

Introduction

1-4

Testing The Significance Of Correlation Coefficient

5

Regression Analysis

6-8

Testing The Significance Of The Slope

9

The Standard Error Of Estimate

10-14

Assumptions Underlying Linear Regression

15-18

Transforming Data

19-22

References

23

INTRODUCTION

Correlation analysis which is a technique used to quantify the associations between two continuous variables. For example, we want to measure the association between hours of exercise per day and the body weight.

Regression analysis is a related technique to evaluate the relationship between outcome variable and one or more risk factors or confounding variables.

The outcome variable is also called the dependent variable, and the risk factors and confounders are called the predictors, or explanatory or independent variables.  The dependent variable is refer to"Y" and the independent variables are refer by "X" in the regression analysis.

CORRELATION ANALYSIS

The sample correlation coefficient, denoted r, ranges between -1 and +1 and measure the direction and strength of the linear association between the two variables(X and Y). The correlation between two variables(X and Y) can be negative and positive .

The sign of the correlation coefficient represent the direction of the association. The magnitude of the correlation coefficient represent the strength of the association.

As example, when a correlation of r that is -0.2 recommend a weak, negative association When a correlation of r that is 0.8 recommendthis is a strong, positive relationship between two variables(X and Y).There is no linear association between two continuous variables(X and Y)when correlation close to zero.

Please be caution , It is important to notice because there may be a non-linear association between two continuous variables(X and Y), but computation of a correlation coefficient does not investigate this. It always important to assess the data intently before computing a correlation coefficient. Graphical illustrate are normally useful to probe associations between variables(X and Y).

[pic 2][pic 3]

[pic 4][pic 5]

[pic 6]

The figure above shows the five types of hypothetical scenarios in which one continuous variable is plotted along the Y-axis and X-axis.

The more closely the points come to a straight line, the stronger is the degree of correlation between the variables(X and Y).The greater the scatter of the plotted points on the chart, the weaker is the relationship between two variables (X and Y).

The coefficient of correlation (r) is +1 when the two variables (X and Y)are strongly positively correlated.

The coefficient of correlation (r) is -1 when the two variables (X and Y)are strongly negative correlated.

[pic 7]

Example For Correlation coefficient

Blood pressure ,y of 8 men and their ages,x,are recorded in the following table.

Ages ,x

(Years)

Blood Pressure,Y(mmHg)

(x-)[pic 8]

(X-[pic 9]

(y-ȳ)

(y-ȳ)²

(x-)(y-ȳ)[pic 10]

Men 1

41

129

-7

49

-6.875

47.266

48.125

Men 2

37

119

-11

121

-16.875

284.766

185.625

Men 3

48

129

0

0

-6.875

47.266

0

Men 4

37

116

-11

121

-19.875

395.016

218.625

Men 5

41

141

-7

49

5.125

26.266

-35.875

Men 6

55

146

7

49

10.125

102.516

70.875

Men 7

66

151

18

324

15.125

228.766

272.25

Men 8

59

156

11

121

20.125

405.016

221.375

∑834

∑1536.878

∑981

...

...

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