 # 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).

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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.

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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-)²[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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