Bjqp2013 – Statistical Technique for Decision Making
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[pic 1]BJQP 2013STATISTICAL TECHNIQUE FOR DECISION MAKINGSEMESTER 1 2017/2018 (A171)GROUP ASSIGNMENTTITLE: CORRELATION AND REGRESION PREPARED FOR: DR. HJ. MOHD AKHIR BIN HJ. AHMADPREPARED BY: No.NameMatric NumberLOKE HUI TENG253848LIM QIAN QIAN254724KHNG ZHING-MEI253614CHUA KELLY253912HANG JIA SIN253940TAN YING LI253847 OBJECTIVEThe objectives of learning correlation and linear regression are:Understanding the uses of correlation analysisCalculate and interpret the correlation coefficient of the relationship between two variables, confidence and prediction. Apply the method of regression analysis and estimate the linear relationship between two variables.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.Using log function to transform a nonlinear relationship to linear relationship.TABLE CONTENTNO.CONTENTPAGESIntroduction1-4Testing The Significance Of Correlation Coefficient5Regression Analysis 6-8Testing The Significance Of The Slope9The Standard Error Of Estimate10-14Assumptions Underlying Linear Regression15-18Transforming Data19-22References23
INTRODUCTIONCorrelation 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 ANALYSISThe 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 coefficientBlood 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 141129-749-6.87547.26648.125Men 237119-11121-16.875284.766185.625Men 34812900-6.87547.2660Men 437116-11121-19.875395.016218.625Men 541141-7495.12526.266-35.875Men 65514674910.125102.51670.875Men 7661511832415.125228.766272.25Men 8591561112120.125405.016221.375∑834∑1536.878∑981