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...

...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...

...
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...

...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 regressionmodel is significant
Goals
(continued)
After this, you should be able to:
• Calculate and interpret confidence intervals for the regressioncoefficients • 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...

...Statistics
ANOVA & Least Squares
Tyrone Sewell
Statistics, MAT 201, Module V-CA5
Alfred Basta
December 20, 2009
Statistics
ANOVA & Least Squares
Look at the data below for the income levels and prices paid for cars for ten people:
| Annual Income Level |Amount Spent on Car |
|38,000 |12,000 |
|40,000 |16,000 |
|117,000 |41,000 |
|17,000 |3,500 |
|23,000 |6,500 |
|79,000 |21,000 |
|33,000 |5,000 |
|66,000 |8,000 |
|15,000 |1,500 |
|52,000 |6,000 |
Answer the following questions:
A. What kind of correlation do you expect to find between annual income and amount spent on car? Will it be positive or negative? Will it be a strong relationship? Base your answer on your personal guess as well as by looking through the data.
The annual income and amount of money spent on a car correlates that generally the greater the sum of income the larger portion of money spent on a car. The middle/low to middle income in datas spent the most with percentages ranging from the low 21% to 40%. The middle/high income percentages took a much smaller...

...direct customers with respect to their warranty policies.
Q9) A company is contemplating to give VRS to its employees. The HR director tells the president that roughly 60% of the employees are eligible for VRS. The president forms a special committee to assess the eligible candidates. The committee conducts in-depth interviews with 120 employees and finds that in its judgment only 70% of the people in samples are qualified for VRS. The president wants to know whether the findings of the human resource director are correct or not. (Test at a significance level of 0.05)
Q10) Toyota wanted to upgrade one of its models for the Indian market. But up gradation definitely meant a higher price charged and with stiff competition in the Indian market, Toyota, was not very sure whether the new upgraded model would impress the customers or not. So before launching the new model, the company wanted to get an idea about the prospective Indian customers.
Q11) It was February 2, 2001 and Alan Green was finishing his first month as an analyst in Pilgrim Bank’s online banking group. The words of his boss Raman, who had just left his office, were lingering in his mind. “There is a meeting with the senior management team to discuss our internet strategy. There is disagreement within the group on whether we should start charging fees to the use of online banking channels or we should come out with schemes which actually increase the use of...

...Economics 141 (Intro to Econometrics) Professor Yang
Spring 2001
Answers to Midterm Test No. 1
1. Consider a regressionmodel of relating Y (the dependent variable) to X (the independent
variable) Yi = (0 + (1Xi+ (i where (i is the stochastic or error term. Suppose that the
estimated regression equation is stated as Yi = (0 + (1Xi and ei is the residual error term.
A. What is ei and define it precisely. Explain how it is related to (i.
ei is the residual error term in the sample regression function and is defined as eI hat = Y
– Y hat.
ei is the estimated error term of the population function.
B. What is (i and define it precisely. What are the four reasons for the inclusion of this error term in the population regression function (model)?
(i is the stochastic term in the population regression function. The four reasons for its existence are: 1. Omitted variable 2. Measurement error 3. Different functional form
4. to account for purely randomness in the human behavior.
C. Draw a graph where you can clearly show E(Yi(XI) = (( + ((XI and Yi = (0 + (1Xi. Show
also in your graph (( and e6 for the X6. This graph graph will show true and estimated
regression lines together with their respective error terms.
See Figure 2.1 on pages 18 (& 39) of the textbook...

...
Simple LinearRegressionModel
1. The following data represent the number of flash drives sold per day at a local computer shop and their prices.
| Price (x) | Units Sold (y) |
| $34 | 3 |
| 36 | 4 |
| 32 | 6 |
| 35 | 5 |
| 30 | 9 |
| 38 | 2 |
| 40 | 1 |
| a. Develop as scatter diagram for these data. b. What does the scatter diagram indicate about the relationship between the two variables? c. Develop the estimated regression equation and explain what the slope of the line indicates. d. Compute the coefficient of determination and comment on the strength of relationship between x and y. e. Compute the sample correlationcoefficient between the price and the number of flash drives sold. f. Perform a t test and determine if the price and the number of flash drives sold are related. Let α = 0.01. g. Perform an F test and determine if the price and the number of flash drives sold are related. Let α = 0.01. |
ANS:
b. Negative linear relationship.
c. | = 29.7857 - 0.7286xThe slope indicates that as the price goes up by $1, the number of units sold goes down by 0.7286 units. |
d. | r 2 = .8556; 85.56% of the variability in y is explained by the linear relationship between x and y. |
e. | rxy = -0.92; negative strong relationship. |
f. t = -5.44 < -4.032 (df = 5); reject Ho, and...

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