This article considers the relationship between two variables in two ways: (1) by using regression analysis and (2) by computing the correlation coefficient. By using the regression model, we can evaluate the magnitude of change in one variable due to a certain change in another variable. For example, an economist can estimate the amount of change in food expenditure due to a certain change in the income of a household by using the regression model. A sociologist may want to estimate the increase in the crime rate due to a particular increase in the unemployment rate. Besides answering these questions, a regression model also helps predict the value of one variable for a given value of another variable. For example, by using the regression line, we can predict the (approximate) food expenditure of a household with a given income. The correlation coefficient, on the other hand, simply tells us how strongly two variables are related. It does not provide any information about the size of the change in one variable as a result of a certain change in the other variable.

Let us return to the example of an economist investigating the relationship between food expenditure and income. What factors or variables does a household consider when deciding how much money it should spend on food every week or every month? Certainly, income of the household is one factor. However, many other variables also affect food expenditure. For instance, the assets owned by the household, the size of the household, the preferences and tastes of household members, and any special dietary needs of household members are some of the variables that influence a household’s decision about food expenditure. These variables are called independent or explanatory variables because they all vary independently, and they explain the variation in food expenditures among different households. In other words, these variables explain why different households spend different amounts of money on food....

...Chapter 4 Simpleregressionmodel Practice problems
Use Chapter 4 Powerpoint question 4.1 to answer the following questions:
1. Report the Eveiw output for regressionmodel .
Please write down your fitted regressionmodel.
2. Are the sign for consistent with your expectation, explain?
3. Hypothesize the sign of the coefficient and test your hypothesis at 5% significance level using t-table.
4. What percentage of variation in 30 year fixed mortgage rate is explained by this model? Why?
Use Chapter 4 Powerpoint question 4.2 to answer the following questions:
5. Report the Eveiw output for regressionmodel
Based on the estimation period of 1986.01 – 1999.07. Please write down your fitted regressionmodel.
6. Is Trend correlated with USPI? Set up the hypothesis testing at 5% significance level.
7. What percentage of variation in USPI is explained by this model? Why?
8. Based on your Eview model, report your forecast of USPI for the period of 1999.08-2000.07. Report RMSE.
Use Chapter 4 Powerpoint question 4.3 to answer the following questions:
9. Report the Eveiw output for regressionmodel USPIt = (USTBR)t + t based on the estimation period of 1986.01 – 1999.07. Please write down your...

...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...

...
• All numerical calculations and graphs/plots should be done using EXCEL.
• A hard copy of your completed assignment must be submitted electronically with the Griffith OUA Cover Sheet (available in the Assessment section of the unit website) attached as the 1st page of your submission. See instruction on the IBA134 Business Statistics unit website under “Assessment” and “Online submission of assignments using SafeAssign” on the link https://learning.secure.griffith.edu.au/webapps/portal/frameset.jsp?tab=courses&url=/bin/common/course.pl?course_id=_111213_1&frame=top
• You assignment must be in a Word doc format – no pdfs!
• When answering questions, wherever required, you should cut and paste the Excel output (eg, plots, regression output etc) to show your working on your assignment.
• You are required to keep a hard copy and an electronic copy of your submitted assignment to re-submit, in case the original submission is lost for some reason.
Important Notice:
As this is an individual assessment item, students should work on their own and present their individual assignment submission. If found to have cheated, all submissions involved would receive a mark of zero for this assessment item.
Discussions related to the assignment will not be allowed on the Discussion Board.
Computer Assignment Problem
Answer all SIX Questions
Some critics of television complain that the amount of violence shown on...

...
SimpleLinearRegressionModel
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 correlation coefficient 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 conclude x and y are related....

...EXECUTIVE SUMMARY
The study is undertaken to study retailers behavior towards Aircel in selected region. The data is collected directly by visiting outlets through structured interview scheduled. The statistical tools used to analyze the data are: Co-relation analysis, SimpleLinearRegression and Multiple LinearRegression. The software used to analyze the data is Windostat version 8.6, developed by Indostat services, is an advanced level statistical software for research and experimental data analysis.
The study is carried mainly in the areas like Lokthkunta, Lalbazar, Kharkhana, Old Alwal, Suraram, Medchal, Miyapur, Balanagar, Bollaram, Yapral, Anandbagh, Malkajgiri, ECIL areas in Hyderabad city.
1. INTRODUCTION
Telecommunication was one of the world powerful tool of development. It is one of the key changer for continuous growth and in areas of reducing poverty, employment development, gender equity, balanced regional development and special protection for vulnerable sections of the society. Indian telecommunication sector has undergone as a growth engine for the Indian economy in the last decade with the country experiencing huge growth in wireless sector. The penetration of internet and broadband has also improved.
Telecom sector is broadly divided into:
1. Fixed line telephony.
2. Mobile telephony.
a. Global System for Mobile Communications (GSM) and
b. Code Division...

...SIMPLE VERSUS MULTIPLE REGRESSION
The difference between simple and multiple regression is similar to the difference between one way and factorial ANOVA. Like one-way ANOVA, simpleregression analysis involves a single independent, or predictor variable and a single dependent, or outcome variable. This is the same number of variables used in a simple correlation analysis. The difference between a Pearson correlation coefficient and a simpleregression analysis is that whereas the correlation does not distinguish between independent and dependent variables, in a regression analysis there is always a designated predictor variable and a designated dependent variable. That is because the purpose of regression analysis is to make predictions about the value of the dependent variable given certain values of the predictor variable. This is a simple extension of a correlation analysis. If I am interested in the relationship between height and weight, for example, I could use simpleregression analysis to answer this question: If I know a man’s height, what would I predict his weight to be? Of course, the accuracy of my prediction will only be as good as my correlation will allow, with stronger correlations leading to more accurate predictions. Therefore, simple...

...Tiffany Camp
ECO-250
Volker Grzimek
Regression Analysis of Work Hours in Relation to GPA
This research investigated the affects of working extra hours in a labor position on students’ GPAs each semester at Berea College. It was my belief that students who worked more hours were more likely to have lower GPAs due to their studying abilities and opportunities being compromised as a result of working too long (a negative correlation or trend between GPAs and hours worked each week). For each hour a student worked it was my belief that he or she became more fatigued, more stressed, and lost an hour in which to study. Each student must work at least ten hours here on campus as required by the Berea College Labor Program. Students may select to work more to make more money or to gain experience in a chosen field, or they may have to work more to meet work requirements for state assistance programs which help them financially but require that certain number of hours (usually 20) be worked by the student each week.
In order to test this hypothesis it was important that I collect unbiased samples. I did so by placing a survey in the labor program office where any random student was just as likely as any other to come in during this time of year when all students were turning in forms for their labor positions for the next year. I asked the students to record their classification (freshman, sophomore, etc.), whether or not they were recent...

...TRUE
2. In a simpleregression analysis the error terms are assumed to be independent and normally distributed with zero mean and constant variance. – TRUE
3. The difference between the actual Y-value and the predicted Y-value found using a regression equation is called the residual (ε) – TRUE
4. In a multiple regression analysis with N observations and k independent variables, the degrees of freedom for the residual error is given by (N-k). – FALSE (correct answer N-k-1)
5. From the following scatter plot, we can say that between y & x there is _______. – Negative correlation
6. According to the graph, X & Y have ________. – Virtually no correlation
7. A cost accountant is developing a regressionmodel to predict the total cost of producing a batch of printed circuit boards as a function of batch size (the number of boards produced in one lot or batch.) The explanatory variable is called the _______. – Coefficient of determination
8. In the regression equation, y = 75.65 + 0.50x, the intercept is ______. – 75.65
9. The assumptions underlying simpleregression analysis include ______. – The error terms are independent
10. The proportion of variability of the dependent variable accounted for or explained by the independent variable is called the _______. – coefficient of determination
11. A...

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