MCQs on Correlation and Regression Analysis with Answers by http://itfeature.com
Chapter14 Multiple Regression and Correlation AnalysisFull description
Report written at the University of Leeds, 2006
statistics
Draper, N., Smith, H. (1998), Applied Regression Analysis, John Wiley, New York.Descripción completa
Draper, N., Smith, H. (1998), Applied Regression Analysis, John Wiley, New York.Full description
Short Note about correlation
Between the two concepts of past life regression and reincarnation, most people are probably more familiar with the latter. However, what few realize is that these two concepts are essentially link...Full description
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hfjyfFull description
test
This is the topic of Simple Regression from the course of Statistical Inferences. This whole presentation is designed and created by the Professor of University Of Management and Technology Lahore,...
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Linear regressionFull description
The Correlation Secret by Jason Fielder How to make the most of your forex trading by understanding forex pair correlation. The secret used by many institutional investors to make substan…Full description
Short research paper on orkiszewski's correlationDescripción completa
Correlation and Regression Analysis
Nayyar Raza Kazmi M.B.,B.S, D.H.P.M, M.P.H, M.Sc
Objectives of the Lecture • To understand the concept of Correlation and Regression Analysis. • Understand the areas in which Correlation and regression Models can be applied. • Understand interpreting Correlation and Regression parameters.
• Most of studies done by Post graduate trainees are crosssectional in nature. • Analysis of such studies is mostly confined to application of descriptive univariate statistics. • Quality of such studies can be enhanced by further data mining by Correlation and Regression Analysis.
Correlation – Strength of association between two variables. – Tells us how much the two variables are associated with one another. – However doesn’t assume CAUSATION. CAUSATION. – Simply tells us whether the two variables are positively or negatively correlated. correlated .
Regression • If there is a strong correlation between two variables, Regression is used to determine the value of dependent variable (Y) from the value of independent variable (X) • Types – Simple Linear Regression – Multiple Linear Regression – Logistic Regression
Correlation Analysis is a group of statistical techniques to measure the association between two variables. Advertising Advertising Minutes and $ Sales
A Scatter Diagram is a chart that portrays the relationship between two variables. The Dependent
Variable is the variable being predicted or estimated.
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The Independent
Variable provides the basis for estimation. It is the predictor variable. variable. Correlation Analysis
The Coefficient of Correlation (r ) is a measure of the strength of the relationship between two variables. Also called Pearson’s r and It requires interval or ratio Pearson’s product moment scaled data. correlation coefficient. P e a r r s o n ' s It can range from -1.00 to 1.00. Values of -1.00 or 1.00 indicate perfect and strong correlation. Negative values indicate an inverse relationship and positive values indicate a direct relationship.
- 1
0
1
Values close to 0.0 indicate weak correlation. The Coefficient of Correlation,
Y
10 9 8 7 6 5 4 3 2 1 0 0
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5 6 X
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Perfect Negative Correlation
Y
10 9 8 7 6 5 4 3 2 1 0 0
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5 6 X
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Perfect Positive Correlation
Y
10 9 8 7 6 5 4 3 2 1 0 0
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Zero Correlation
Phi Co-efficient • Used for two categorical variables
Ф =
ad - bc (a+b)(a+c)(c+d)(b+d)
Regression Equation and Regression Line Y
c
=
a
+
bX
• where Y = computed value of the dependent variable a c = Y -intercept -intercept where X equals zero • = slope of the the regression line, which is the increase or decrease b • in Y for each change of one unit of X X X = a given value of the independent variable •
Simple Linear Regression • Determines the value of a Dependent Variable based on a single independent Variable. • Simplest form of Regression Analysis.
Multiple Linear Regression • Used when the Dependent Variable is a continuous variable and independent variables are continuous or categorical.
Y = a + b1 x 1 + b2 x 2+……..+bk x k
Putting MLR in Practice • A descriptive study on normal healthy adults aged 14-25 years gathers date about their weight, systolic Blood Pressure and Serum Cholesterol levels.
????? • Is serum cholesterol level associated with weight and systolic blood pressure? • Can we predict Serum Cholesterol levels if we know a persons weight and systolic blood pressure.
Y = a + b1 x 1 + b2 x 2+……..+bk x k Y= 18.52+3.20(BP)+[-4.06(Weight)] So What could be the Serum Cholesterol level for a person who weighs 75Kg and has a systolic Blood Pressure of 145mm Hg????
Logistic Regression • Logistic Regression is used when the outcome variable is categorical • The independent variables could be either categorical or continuous continuous • Logistic Regression determines the Odds Ratio for various independent variables for the dichotomous dichotomous dependent variable
• The Dichotomous Dependent variable could be presence/ absence of a complication, disease etc. • Data for dichotomous variables must be binary coded like 1 for presence of complication or disease and 0 for Absence of complication or disease.
Putting Logistic Regression in Practice • Risk Factors for Complications of Diabetes Mellitus in patients admitted to a Tertiary Care Hospital
What can I derive from this Data??????
Risk Factors for No of patients Retinopathy (n=32)
%age
BMI> 30
13
40.26
Smoking
28
87.5
Level of prior awareness
14
43.75
HbA1C >7
10
31.25
Duration of Diabetes > 10 Years
20
62.5
Where Correlation and Regression Models can be applied • Cross-sectional studies. • K.A.P Studies • Studies aiming to determine relationships between certain factors of interest and their outcomes
Softwares to use • MS Excel with Data Analysis add-in installed • SPSS • Epi Info 2002 • MedCalc (Recommended because of ease of use and power to perform all types of statistical calculations)
• Thankyou for your patience.(There is a Negative Strong Correlation between length of Biostats lecture and the Your moods evident by the 11 “O” Clock sign on your forheads • Questions, Queries and Suggestions are welcome.
