This website uses cookies to ensure you have the best experience.

1773 words - 8 pages

MSOR 221 Statistical Inference

Chapter 18 Multiple Regression

Model and Required Conditions

For k independent variables (predicting variables) x1, x2, … , xk, the multiple linear regression model is represented by the following equation:

[pic]

where (1, (2, … , (k are population regression coefficients of x1, x2, … , xk respectively, (0 is the constant term, and ( (the Greek letter epsilon) represents the random term (also called the error variable) – the difference between the actual value of Y and the estimated value of Y based on the values of the independent variables. The random term thus accounts for all other independent variables that are not included in the model.
...view middle of the document...

55 |
| |3 |100 |100 |300 |10000 |300 |9 |10000 |95.92 |
| |10 |600 |400 |4000 |240000 |6000 |100 |360000 |379.61 |
| |33 |2800 |1500 |10300 |880000 |18800 |235 |1700000 |1500 |

n = 6

[pic]

By solving the above system of normal equations, we should find the following:

b0 = 6.397 b1 = 20.492 b2 = 0.280

( The sample multiple linear regression equation is:
[pic]

Interpretation of the Regression Coefficients

b1: the approximate change in y if x1 is increased by 1 unit and x2 is held constant.
b2: the approximate change in y if x2 is increased by 1 unit and x1 is held constant.

In Example 1, if x1 is increased by 1 unit and x2 is held constant, then the approximate change in y therefore will be 20.492 units.

Point Estimate

In Example 1, suppose x1 = 4 and x2 = 500, then the point estimate of y equals:
[pic]

The Standard Error of Estimate in Multiple Regression Model

[pic]

where [pic] = the observed y value in the sample
[pic] = the estimated y value calculated from the multiple regression equation

|In Example 1, |[pic] | | | |
| |(17.01)2 | |[pic] |
| |(-5.2)2 | | |
| |(5.27)2 | | |
| |(-41.55)2 | | |
| |(4.08)2 | | |
| |(20.39)2 | | |
| |2502.954 | | | |

Note: [pic] is the point estimate of [pic](the standard deviation of the error variable (.)

Testing the Validity of the Model – The Analysis of Variance (ANOVA) Test

Let’s consider a simple linear regression model:

y

* [pic]= (y / n = the mean of y

* *
[pic]
* *

x

[pic]
← [pic]

[pic] = total deviations
[pic] = total deviations of estimated values from the mean
[pic] = error deviations = [pic]
[pic] = the residual of the ith data point

[pic]
← SST = SSR + SSE
SST = total sum of squared deviations = total variation
SSR = sum of squares resulting from regression = explained variation
SSE = sum of squares...

Math 533 Final Essay

1887 words - 8 pages MATH/GM 533 Final Exam 1. (TCO D) PuttingPeople2Work has a growing business placing out-of-work MBAs. They claim they can place a client in a job in their field in less than 36 weeks. You are given the following data from a sample. Sample size: 100 Population standard deviation: 5 Sample mean: 34.2 Formulate a hypothesis test to evaluate the claim. (Points : 10)         Ho: µ = 36; Ha: µ ≠ 36        Ho: µ ≥ 36; Ha: µ < 36        Ho

Math Essay

634 words - 3 pages This article is about the study of topics, such as quantity and structure. For other uses, see Mathematics (disambiguation). "Math" redirects here. For other uses, see Math (disambiguation). Euclid (holding calipers), Greek mathematician, 3rd century BC, as imagined by Raphael in this detail from The School of Athens. Mathematics is the study of topics such as quantity (numbers), structure, space, and change. There is a

Math

682 words - 3 pages Matematik aflevering Af Emil Dokkedahl Opgave 7 (3) Nedenstående tabel viser en opgørelse over det årlige antal reklametimer, der blev vist på de danske tv-kanaler i perioden 2000-2010. I en model kan udviklingen i det årlige antal reklametimer på de danske tv-kanaler beskrives ved hvor er det årlige antal reklametimer på de danske tv-kanaler, og t er antal år efter 2000. Opgave a Jeg definere mine værdier Jeg bestemmer a

Math

7824 words - 32 pages MA1200 Basic Calculus and Linear Algebra I Lecture Note 1 Coordinate Geometry and Conic Sections υ MA1200 Basic Calculus and Linear Algebra I Lecture Note 1: Coordinate Geometry and Conic Sections Topic Covered • Two representations of coordinate systems: Cartesian coordinates [ሺ‫ݕ ,ݔ‬ሻcoordinates] and Polar coordinates [ሺ‫ߠ ,ݎ‬ሻ-coordinates]. • Conic Sections: Circle, Ellipse, Parabola and Hyperbola. • Classify the conic

Accounting Math

1092 words - 5 pages improvements (Shaviro, 1997). Respectfully, Problem P3-2A Neosho River Resort, Inc. opened for business on June 1 with eight air-conditioned unties. Its trial balance before adjustments on August 31 is as follows. Neosho River Resort, Inc.Trial BalanceAugust 31, 2008 | Account Number | | Debit | Credit | 101 | Cash | 19,600 | | 126 | Supplies | 3,300 | | 130 | Prepaid Insurance | 6,000 | | 140 | Land | 25,000 | | 143

Math Algebra

538 words - 3 pages A. Solve the following questions involving fundamental operations on polynomials A .Find p(x) + 4q(x) given p(x)= 4x4 + 10x3 - 2x2 + 13 and q(x) = 2x4+ 5x2 - 3 p(x) + 4q(x) = 4x4 + 10x3 - 2x2 + 13 + 8x4+ 20x2 â€“ 12 = 12x4 + 10x3 + 18x2 + 1 b. Find P(-1/2) if P(x) = 2x4 + x3 + 12 P(-1/2) = 2(-1/2)4 + (-1/2)3 + 12 = 12 c. Simplify: (-4 + x2 + 2x3) â€“ (-6 â€“ x + 3x3) â€“ (-6y3 + y2) = -4 + x2 + 2x3 + 6 + x - 3x3 + 6y3 - y2 = 2 + x

Teaching Math

1090 words - 5 pages motivation may profit from rewards. Shorter homework is better than long homework, and group homework is sometimes effective, though these findings depend on grade level. Homework helps simple skills, but not broader measures of achievement. Bilingualism Most bilingual adults switch languages when calculating. Such code-switching has no impact on math ability and should not be discouraged. Learning statistics When studying statistics

Math Investigation

4261 words - 18 pages Math Investigation of Painted Cubes Introduction I was given a brief to investigate the number of faces on a cube, which measured 20 small cubes by 20 small cubes by 20 small cubes (20 x 20 x 20). To do this, I had to imagine that there was a very large cube, which had had its outer surface painted red. When it was dry, the large cube was cut up into the smaller cubes, all 8000 of them. From there, I had to answer the question, 'How

Math Investigation

1863 words - 8 pages OBLONG, OBLONG WHERE DO WE BELONG? (Oblong Numbers) I. Introduction Math investigations engage one’s mind to formulate conjectures from observed numerical phenomenon. Patterns are being observed and these patterns are then translated into mathematical expressions such as the equation. Thus this investigation would lead to mathematical models that need to be proven. However, the formulation of a mathematical model is not an

Discrete Math

1740 words - 7 pages Lecture 1. Logic. Propositions. The rules of logic specify the precise meaning of mathematical statements. For instance, the rules give us the meaning of such statements as, “There exists an integer that is greater than 100 that is a power of 2”, and “For every integer n the sum of the positive integers not exceeding n is ”. Logic is the basis of all mathematical reasoning, and it has practical applications to the design of computing machines, to

Math Assistance

1065 words - 5 pages 1-68. Assume 6,000 children go to Disneyland today. How much additional revenue will Disneyland receive if it raises the cost of admission from \$31 to \$41 and lowers the age limit for adults from 12 years old to 10 years old? 2-34. Joy Wigens, who works at Putnam Investments, received a check for \$1,600. She deposited ¼ of the check in her Citibank account. How much money does Joy have left after the deposit? 2-36. Lester bought a

Related Essays

Fuzzy Math Essay

750 words - 3 pages FUZZY MATH BUSINESS CASE Prof: Sandra Malach Student: Adam Fehr ID: 10115447 Joe Davis is a new hire and as such he has not figured out the exact inner workings of the company. With his limited experience he has already witnessed what he has thought to be a lack of ethical and accounting practices. Gallagher and MacDonald do not seem to care about their clients and are only focused on paying the lowest possible penalties to Symbol. Joe

Math Is Hard Bro Essay

1329 words - 6 pages University of Phoenix Material Sustainability Problems The MTH/209 Week Five Learning Team assignment requires each team to select a scenario and explain how algebraic concepts underlie sustainable environmental, business, or human health practices. Concept of Sustainability Sustainability may broadly be defined as the ability of any system to sustain itself. Sustainability principles can apply to many areas, including human health

Quiz 2 Math 540 Essay

1152 words - 5 pages Quiz 2 Math 540 • Question 1 2 out of 2 points If two events are not mutually exclusive, then P(A or B) = P(A) + P(B) Answer Selected Answer: False Correct Answer: False • Question 2 2 out of 2 points Probability trees are used only to compute conditional probabilities. Answer Selected Answer: False Correct Answer: False • Question 3 2 out of 2 points Seventy two percent of all

Math 156 Reflection Essay

674 words - 3 pages that were made. Data analysis encompasses many different techniques across many different subjects like math, science, and business. Probability is not an exact science, but is instead based on the conclusions of what will most likely happen. To calculate probabilities it is important to look at the whole picture. Geometry is the study of shapes, their size, positioning, and type like two dimensional and three dimensional. Geometry is all around us