Project 1: Linear Correlation and Regression Analysis

Gross Revenue and TV advertising:

Pfizer Inc, along with other pharmaceutical companies, has begun investing more promotion dollars into television advertising. Data collected over a two year period, shows the amount of money Pfizer spent on television advertising and the revenue generated, all on a monthly bases.

The objective of this report is to conduct a correlation and regression analysis that studies the relationship between Revenue and TV advertising in arriving at a mathematical equation that can help to understand and forecast...

...Introduction to LinearRegression and CorrelationAnalysis
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 regressionanalysis 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 regressionanalysis applications for purposes of prediction and description • Recognize some potential problems if regressionanalysis 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 • Correlationanalysis 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...

...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 Linearregression and correlation In linearregression, 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 linearregression model by computing either manually or using Excel. 3. Compute the correlation coefficient and comment the correlation between variables. 4. Make hypothesis if there is relationship between the variables. To be easier, in this section you should...

...13
CORRELATION AND REGRESSIONANALYSIS
OUTLINE
4.1 Definition of CorrelationAnalysis
4.2 Scatter Diagram and Types of Relationships
4.3 Correlation Coefficient
4.4 Interpretation of Correlation Coefficient
4.5 Definition of RegressionAnalysis
4.6 Dependent and Independent Variables
4.7 Simple LinearRegression: Least Squares Method
4.8 Using the simple LinearRegression equation
4.9 Cautionary Notes and Limitations
OBJECTIVES
By the end of this chapter, you will be able to:
1 determine the strength and nature of the association between the variables.
2 interpret the observed relationship between the variables of interest.
3 estimate possible outcome of an unknown variable upon the knowledge of the value of the variables and the relationship between the variables.
INTRODUCTION
By observation, we may notice that certain variables seem to be related or associated in some way and to some degree. For example, there may be relationships between number of hours spent on studying and the grades attained in examination; income earned and amount spent on entertainment.
CorrelationAnalysis and RegressionAnalysis are statistical techniques that study the relationships that exist...

...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 correlationanalysis referred to as the dependent and determination variables.
Answer: False Difficulty: Easy Goal: 1
5. Correlationanalysis 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 correlationanalysis is to find how strong the relationship is between two variables.
Answer: True Difficulty: Easy Goal: 2
7....

...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...

...
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 RegressionAnalysis is the equation that allows one to estimate the value of one variable based on the value of another.
Key objectives in performing a regressionanalysis 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...

...Linear-RegressionAnalysis
Introduction
Whitner Autoplex located in Raytown, Missouri, is one of the AutoUSA dealerships. Whitner Autoplex includes Pontiac, GMC, and Buick franchises as well as a BMW store. Using data found on the AutoUSA website, Team D will use LinearRegressionAnalysis to determine whether the purchase price of a vehicle purchased from Whitner Autoplex increases as the age of the consumer purchasing the vehicle increases. The data set provided information about the purchasing price of 80 domestic and imported automobiles at Whitner Autoplex as well as the age of the consumers purchasing the vehicles. Team D selected the first 30 of the sampled domestic vehicles to use for this test. The business research question Team D will answer is: Does the purchase price of a consumer increase as the age of the consumer increases? Team D will use a linear-regressionanalysis to test the age of the consumers and the prices of the vehicles.
Five Step Hypothesis Testing
Team D will conduct the two-sample hypothesis using the following five steps:
1. Formulate the hypothesis
2. State the decision rule
3. Calculate the Test Statistic
4. Make the decision
5. Interpret the results
Step 1- Formulate the Hypothesis
Using the research question: Does the purchase price of an automobile purchased at...

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