UNIVERSITI MALAYSIA PERLIS GROUP ASSIGNMENT EQT 271 ENGINEERING STATISTICS SEMESTER 2 SESSION 2012/2013

INSTRUCTIONS: 1. 2. 3. 4. Maximum of 5 persons in a group (should be in the same program). Due date: 28 MAY 2013. Report must be typewritten using A4 paper. The front cover for the report is as in Appendix 1.

In this assignment, you will apply concepts of data approximation and fitting to some real data generated from your surveys. Each modeling tool gives you another way to represent, simplify and make decisions about the real system you are dealing with. You will compute basic statistics of the data and make some statements about basic relationships between variables. For example; could height be related to weight? The report must include: 1. 2. 3. 4. Introduction Methodology Data Analysis Result and Conclusion

1.0 Introduction In your introduction section, you should have a briefly introduction about the background of your research. 2.0 Methodology 2.1 Collecting Data Collecting data can be in two ways; get data from your experiment in the lab and do survey! So what you should have in your data? Your variable must be more than one and your data must be in sample greater than 30. 2.2 Methodology and Data Analysis 2.2.1 Basic Statistics Your calculation for basic statistics must be in Excel and compute the mean, median, standard deviation. Also, you must develop a histogram using Excel.

1

EQT 271 Engineering Statistics

2.2.2 Linear regression and correlation In linear regression, you should follows those instructions: 1. Choose one pair variables, first create the scatterplot (using Excel). Do this by simply plotting one variable as the x –axis and the other y-axis. Based on the scatterplot, comment on the relationship after fitting a simple curve, so you can be creative in pairing the variables. 2. Find the linear regression model by computing either manually or using Excel. 3. Compute the correlation...

...Introduction to LinearRegression and Correlation Analysis
Goals
After this, you should be able to:
• • • • •
Calculate and interpret the simple correlation between two variables
Determine whether the correlation is significant Calculate and interpret the simple linearregression equation for a set of data Understand the assumptions behind regression analysis Determine whether a regression model is significant
Goals
(continued)
After this, you should be able to:
• Calculate and interpret confidence intervals for the regression coefficients • Recognize regression analysis applications for purposes of prediction and description • Recognize some potential problems if regression analysis is used incorrectly • Recognize nonlinear relationships between two variables
Scatter Plots and Correlation
• A scatter plot (or scatter diagram) is used to show the relationship between two variables • Correlation analysis is used to measure strength of the association (linear relationship) between two variables – Only concerned with strength of the relationship – No causal effect is implied
Scatter Plot Examples
Linear relationships y y Curvilinear relationships
x y y
x
x
x
Scatter Plot Examples
(continued)
Strong...

...
CORRELATION
Md. Musa Khan
Lecturer
DBA, IIUC
musa_stat@yahoo.com
Definition:
If two or more variables vary in such a way that change in one are accompanied by changes in the other, these variables are said to be correlated. For example, here exists some relationship between family income and expenditure on luxury items, price of a commodity and amount demanded, increase in rainfall up to a point and production of a rice, etc. The statistical tool with the help of which these relationships between two or more than two variables is studied is called correlation. Therefore the relationship between two or more variables is called correlation.
Co-efficient of correlation:
The measure of correlation is called the coefficient of correlation summarizes in one figure the direction and degree of correlation. It is denoted by r.
Types of correlation:
There are four types of correlations. They are
i. Simple correlation
ii. Multiple...

...LinearRegression deals with the numerical measures to express the relationship between two variables. Relationships between variables can either be strong or weak or even direct or inverse. A few examples may be the amount McDonald’s spends on advertising per month and the amount of total sales in a month. Additionally the amount of study time one puts toward this statistics in comparison to the grades they receive may be analyzed using theregression method. The formal definition of Regression Analysis is the equation that allows one to estimate the value of one variable based on the value of another.
Key objectives in performing a regression analysis include estimating the dependent variable Y based on a selected value of the independent variable X. To explain, Nike could possibly measurer how much they spend on celebrity endorsements and the affect it has on sales in a month. When measuring, the amount spent celebrity endorsements would be the independent X variable. Without the X variable, Y would be impossible to estimate. The general from of the regression equation is Y hat "=a + bX" where Y hat is the estimated value of the estimated value of the Y variable for a selected X value. a represents the Y-Intercept, therefore, it is the estimated value of Y when X=0. Furthermore, b is the slope of the line or the average change in Y hat for each change of one unit in the independent...

...(TYPES OF PROMOTIONAL SCHEMES)
MU1 =MEAN SALE FROM CASH DISCOUNTS
MU2- MEAN SALES FROM FREE GIFTS
CORRELATION AND REGRESSION ASSIGNMENT
These days we have seen huge budgets are allocated to advertising and sales promotions by companies with aim of increasing sales and thereby increasing net profits of the company. I want to analyze how much are these expenses and profits are correlated i.e. to what extent profits depend upon advertising of the company. For this I have taken up Hindustan Uniliver Limited Company which spends significant amount of money on advertising.
Following is the reference to balance sheets of HUL for last ten financial years from where data of Profit after tax and Advertising and sales promotion expense have been taken.
For FY 04-05 please go to Page 84 for Net Profit and Page 87 for advertising and sales expenses.
For FY 06-07 please go to Page 96 for Net Profit and Page 99 for advertising and sales expenses.
For FY 07-08 please go to Page 111 for Net Profit and Page 119 for advertising and sales expenses.
For FY 09-10 please go to Page 121 for Net Profit and Page 139 for advertising and sales expenses.
For FY 11-12 please go to Page 121 for Net Profit and Page 139 for advertising and sales expenses.
For FY 13-14 please go to Page 131 for Net Profit and Page 152 for advertising and sales expenses.
Objective: Understanding correlation between Net profits of the company and advertising...

...Chapter 13
LinearRegression and Correlation
True/False
1. If a scatter diagram shows very little scatter about a straight line drawn through the plots, it indicates a rather weak correlation.
Answer: False Difficulty: Easy Goal: 1
2. A scatter diagram is a chart that portrays the correlation between a dependent variable and an independent variable.
Answer: True Difficulty: Easy Goal: 1 AACSB: AS
3. An economist is interested in predicting the unemployment rate based on gross domestic product. Since the economist is interested in predicting unemployment, the independent variable is gross domestic product.
Answer: True Difficulty: Medium Goal: 1 AACSB: REF
4. There are two variables in correlation analysis referred to as the dependent and determination variables.
Answer: False Difficulty: Easy Goal: 1
5. Correlation analysis is a group of statistical techniques used to measure the strength of the relationship (correlation) between two variables.
Answer: True Difficulty: Easy Goal: 2 AACSB: AS
6. The purpose of correlation analysis is to find how strong the relationship is between two variables.
Answer: True Difficulty: Easy Goal: 2
7. Originated by Karl Pearson about 1900, the...

...1 CORRELATION & REGRESSION
1.0 Introduction
Correlation and regression are concerned with measuring the linear relationship between two variables.
1.1 Scattergram
It is not a graph at all, it looks at first glance like a series of dots placed haphazardly on a sheet of graph paper.
The purpose of scattergram is to illustrate diagrammatically any relationship between two variables.
(a) If the variables are related, what kind of relationship it is, linear or nonlinear ?
(b) If the relationship is linear, the scattergram will show whether it is negative or positive.
1.2 Regression
It is used to identify the precise form of linear relationship between the two variables.
This is done by estimating the equation
Y = a + bx
Where Y is the dependent variable
x is the independent or explanatory variable
a is the regression constant or intercept
b is the slope or regression coefficient
In another words, it is concerned with developing the linear equation by which the value of a dependent variable Y can be estimated from a value of an independent variable.
The regression equation is most frequently found by using least square method (for which the sum of the squared deviations between the actual and...

...Linear -------------------------------------------------
Important
EXERCISE 27 SIMPLE LINEARREGRESSION
STATISTICAL TECHNIQUE IN REVIEW
Linearregression provides a means to estimate or predict the value of a dependent variable based on the value of one or more independent variables. The regression equation is a mathematical expression of a causal proposition emerging from a theoretical framework. The linkage between the theoretical statement and the equation is made prior to data collection and analysis. Linearregression is a statistical method of estimating the expected value of one variable, y, given the value of another variable, x. The term simple linearregression refers to the use of one independent variable, x, to predict one dependent variable, y.
The regression line is usually plotted on a graph, with the horizontal axis representing x (the independent or predictor variable) and the vertical axis representing the y (the dependent or predicted variable) (see Figure 27-1). The value represented by the letter a is referred to as the y intercept or the point where the regression line crosses or intercepts the y-axis. At this point on the regression line, x = 0. The value represented by the letter b is referred to as the slope, or the coefficient of x. The slope determines the...

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