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# Linear Regression and Statistics

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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 percentage rate at 12% and 35%. While the low income percentages represented only 10% of their incomes spent toward a new car purchase. The trend makes the graph ascend on both sides of the linear regression line.

When the incomes of the consumer increase the sales for cars also rises presenting a positive result. Therefore, as long as the incomes continue to grow the relationship to car sales will also trend to the right in an upward, positive motion. B. What is the direction of causality in this relationship - i. e. does having a more expensive car make you earn more money, or does earning more money make you spend more on your car? In other words, define one of these variables as your dependent variable (Y) and one as your independent variable (X).

Depending on the each individuals perspective the variable can switch between dependent and independent based on the person’s viewpoint. For this purpose, the independent variable which is represented by (X) is the annual income. The dependent variable is represented by (Y) and is the cost of the car. The reason I chose to have the annual income as the independent variable is because a person will continue to look for a job with security, growth potential, and a higher income. The car is seen as a vehicle of transportation only and needed to get to work and home.

It is a necessity, but not a luxury item with elaborate expenses. We can have the basic model without all the bells and whistles to accomplish the task to get to and from a location. C. What method do you think would be best for testing the relationship between your dependent and independent variable, ANOVA or regression? Explain your reasoning thoroughly with a discussion of both methods. Both linear regression which utilizes hypothesis testing and ANOVA can be sources for testing. Each testing has its own drawbacks.

In this paper I have utilized the regression calculator. What is hypothesis testing? It is statistical procedures that utilize sample data gathered and then formulates a hypothesis based on the validation of the hypothesis. A hypothesis is an unapproved scientific conclusion drawn from known facts and in statistics an idea, an assumption or theory about certain data with one or more variables that exists in one or more populations. There must be two statements; which represents the population being studied and the alternate. It is assumed the first statement is true.

There are a variety of factors that can contribute to falsifying the conditions. The data gathered can be endless, so setting boundaries is important. An ANOVA (Analysis of Variance) is a tool used for analyzing data, which is a result of a one-way design, and certain assumptions. This technique is used to analyze the variation in the data to determine if more than two population means are equal. A one-way ANOVA has several different levels of one factor being studied and the objects or people being observed and/or measured are randomly assigned to one of the c levels of the factor.

The three major assumptions of an ANOVA are as follows; the errors are random and independent of each other, all of the populations have the same variance, and each population has a normal distribution. D. Top of Form Accuracy The algorithm is written to round all output to no more than11 significant digits. Further, all numbers of magnitude less that 10-12 are presented as zero. The Regression Equation will appear below.

Bottom of Form Last Updated: April, 1999 Copyright © 1999 Stefan Waner and Steven R. Costenoble References Dobson A. , & Young A. & Gibberd B. (n. d. ). SurfStat Australia. Retrieved December 16, 2009, from https://surfstat. anu. edu. au/surfstat-home/surfstat-main. html Graphic demonstration of regression, Retrieved December 20, 2009, from https://www. stattucino. com/berrie/dsl/regression/regression. html Introduction to Analysis of Variance, Retrieved December 16, 2009, from https://onlinestatbook. com/chapter13/intro. html Understanding ANOVA Visually, Retrieved December 20, 2009, from https://www. psych. utah. edu/stat/introstats/anovaflash. html

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