Interpolation, Extrapolation, and Regression

Interpolation is a method of constructing new data points within the range of a discrete set of known data points. It is often required to interpolate the value of that function for an intermediate value of independent variable. This can be achieved by curve fitting or regression analysis. There are many different interpolation methods. Some examples of this include piecewise constant interpolation, linear interpolation, polynomial interpolation, spline interpolation and Gaussian processes. Other forms of interpolation can be constructed by picking a different class of interpolates.

Extrapolation is the process of estimating, beyond the original observation intervals, the value of a variable on the basis of its relationship with another variable. Extrapolation is similar to interpolation. However extrapolation is subject to greater uncertainty and a higher risk of producing meaningless results. Like interpolation, extrapolation uses a variety of techniques that require prior knowledge of the process that created the existing data points. These techniques include linear extrapolation, polynomial extrapolation, conic extrapolation and French curve extrapolation. Typically the quality of a particular method of extrapolation is limited by the assumptions about the function made by the method.

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Regression analysis is a statistical process for estimating the relationships among variables. Regression includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. Regression analysis helps one understand how the typical value of the dependent variable changes when any one of the independent variables is varied which the other independent variable are held at a fixed value. Regression analysis is widely used for prediction and forecasting, where its use has substantial overlap with the field of machine learning.

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Forecast Analysis: Food Price Index
The following table shows six years of average annual food price index (May to April data): Year Annual Food Price Index 2005 101.8 2006 114.8 2007 143.3 2008 144.3 2009 138.1 2010 165.1 (a) Forecast the average annual food price index for all years from 2008 to 2011. Use a three-year weighted moving

A Divided Differences Table and Newton Interpolating Polynomials
Augment the divided differences table in order to find the Newton interpolating polynomial for points(-2,3),(1,6),(2,11) and (-1,2). Do you notice anything interesting about the answer? Can you explain why get this answer?

Maximal Interval of Existence.
Please solve the following ODE problem: For every nonzero xo belonging to R, find the maximal interval of existence of the following initial problem: x’ = f(x) , x(0) = xo , where f: R{0} into R and f(x) = 1/x^2 . Guive proofs for your result. Skectch the region.

Linear Interpolation
Please explain the steps on how to solve the problem below. The accompanying table lists the area of a circle corresponding to several values of the diameter. Find the area corresponding to a diameter of 15 in. by linear interpolation. Diameter x | 0 | 4 | 8 | 12 | 16 | 20

Marketing Consulting Firm
Complete Microsoft Excel problems “Computer Exercise 2 and 3″ in the attachment. Please show your work in Microsoft Excel.

Correlation and Simple Linear Regression
Take your data and arrange it in the order you collected it. The amount of minutes that I have read in a 10 day period 20, 10, 17, 20, 60, 0, 30, 0, 0, 0 Count the total number of observations you have, and label this number N. Then create another set of data starting from one and increasing by one until you reach N.

Correlation and Simple Linear Regression
1. Find the equation of the regression line for the given data. Predict the value of Y when X=-2? Predict the value of Y when X = 4? x -5 -3 4 1 -1 -2 0 2 3 -4 y -10 -8 9 1 -2 -6 -1 3 6 -8 2. The data below are the final exam scores of 10 randomly selected statistics students and the number of hours they studied for t

Correlation Coefficient & Linear Regression Analysis
1. Find the equation of the regression line for the given data. Predict the value of Y when X=-2? Predict the value of Y when X = 4? x -5 -3 4 1 -1 -2 0 2 3 -4 y -10 -8 9 1 -2 -6 -1 3 6 -8 2. The data below are the final exam scores of 10 randomly selected statistics students and the number of hours they studied for th

Regression and Correlation
Regression and correlation. Pick any two columns that have a correlation coefficient greater than 0.6 or less than -0.6. Pick the one with the highest absolute value. (attached xls) a. Draw the scatter diagram of Y against X, and explain any noted significance. b. Compute correlation coefficient (Ã?Â? or r), and what d

Regression analysis.
Fertilizer Yield 0 6 0 9 20 19 20 24 40 32 40 38 60 46 60 50 80 48 80 54 100 52 100 58 When applied a quadratic term on fertilizer and performed the quadratic regression analysis, what is b2? a) 6.6429 b) 0.8950 c) -0.00407 Is the curvilinear effect significant?

Simple Linear Regression Analysis
In normal circumstances, the zoo may be able to achieve its target goal and attract an annual attendance equal to 40% of its community. Approximately 35% of all visitors are adults. Children accounted for one-half of the paid attendance. Group admissions remain a constant 15% of zoo attendance. Due to its northern climate, t

Regression Analysis
A large consumer product company wants to measure the effectiveness of different types of advertising media in the promotion of its products. Specifically, two types of advertising media are to be considered: radio/TV advertising and newspaper advertising (including the cost of discount coupons). The sales of product (in thousan

Unweighted and Weighted Linear Regression
See the attached fie. a) Consider the following set of regression equations: Y1 = βx1 + e1 Y2 = βx2+ e2 .. Yn = βxn + en Suppose also that w1, w2, …, wn are a set of positive weights (known constants). Consider the function f(β) = ∑ wiei2 = ∑ wi (yi – βxi)2 Find the value of β that minimiz

Northern White Rhinoceros Population in the 1970s
In the 1980s, the Northern white rhinoceros population decreased by 485 from what it was in the 1970s. by the 1990s the population increased to 2 more than twice the population in the 1970s. by 2000s, the population dropped 25 rhinoceroses to about 977 northern white rhinoceroses today. What was the northern white rhinoceros pop

Regression Equation and Statistical Methodologies
Using the attached document: (A) Analyze the above output to determine the regression equation. (B) What conclusions are possible using the meaning of b0 (intercept) and b1 (regression coefficient) in this problem? (That is, explain the meaning of the coefficients.) (C) What conclusions are possible using the coefficien

Linear Regression Analysis & ANOVA
Use ANOVA and REGRESSION for the following problems. 1. Divide your data in half, your first 8 observations and your last 7 observations. Then use ANOVA to test to see if there is a significant difference between the two halves of your data. 2. Take your data and arrange it in the order you collected it. Count the total num

Find solutions.
7. A taxicab company manager believes that the monthly repair costs (y) of cabs are related to age (x) of the cabs. Eight cabs are selected randomly and from their records we obtained the following data:  x =134,  y = 410,  x2 =3 020, y2=24000, and  xy =8340. Estimate the linear regressi

Regression Model
In a regression model, if every sample point is on the regression line (all errors are 0), then a. the correlation coefficient would be 0. b. the correlation coefficient would be -1 or 1. c. the coefficient of determination would be -1. d. the coefficient of determination would be 0.

the correlation coefficient and coefficient of determination
If every sample data point were on the regression line, which of the following would be true? Please explain the correct answer. a. MSE = 0 b. MAD = 1 c. Coefficient of determination = 0 d. Correlation coefficient = 0.5

Examine two groups of numbers using ANOVA and time series regression
These are my numbers: First set of numbers: 26 19 21 15 23 22 18 24 16 19 Second set of numbers: 32 28 21 19 27 1. Divide your data in half, your first 8 observations and your last 7 observations. Then use ANOVA to test to see if there is a significant difference between the two halves of your data. Th

What is the purpose of using regression analysis?
What is the purpose of using regression analysis? How might a regression analysis be used to formulate strategies? Provide examples related to strategy formulation and implementation.

Equation of the regression line
1. Find the equation of the regression line for the given data. 2. The data below are the final exam scores of 10 randomly selected statistics students and the number of hours they studied for the exam. Find the equation of the regression line for the given data.

Regression Equations and Meanings
Scenario: Regression equations are created by modeling data, such as the following: Sales = (Cost Per Item – Number of Items) – Constant Charges In this equation, constant charges may be rent, salaries, or other fixed costs. This includes anything that you have to pay for periodically as a business owner. This value is neg

Regression Analysis
1. The manager of Erehwon police department motor pool wants to develop a forecast model for annual maintenance costs on police cars, based on mileage in the past year, and age of cars. The following data have been collected for eight different cars: Miles Driven Car Age (yr.) Maintenance Cost ($) 16,320

Zagat’s publishes restaurant ratings for various locations in the United States. The file RESTRATE.xls contains the Zagat rating for food, décor, service, and the price per person for a sample of 53 restaurants located in New York City and 53 restaurants located in Long Island. Suppose you wanted to develop a regression model to predict the price per person based on a variable that represents the sum of the ratings for food, décor, and service. Using EXCEL or PHStat2, answer the following: The following is a minimum guideline about what you should analyze. For example, you may have to use such tools as confidence interval estimates, one or two-sample tests on the data to improve the quality of your report. Multiple Regression Analysis is used alongside EDA.
Zagat’s publishes restaurant ratings for various locations in the United States. The file RESTRATE.xls contains the Zagat rating for food, décor, service, and the price per person for a sample of 53 restaurants located in New York City and 53 restaurants located in Long Island. Suppose you wanted to develop a regression mode

Multiple Regression Analysis explained in this solution
A collector of antique grandfather clocks believes that the price (in dollars) received for the clocks at an antique auction increases with the age of the clocks and with the number of bidders. Thus the model is hypothesized is where Y = auction price, x1 = age of clock (years) and x2 = number of bidders. A sample of 32 auct

Math
It has been hypothesized that average thrust can be used as a basis for predicting the cost of rocket engines. It has been further hypothesized that average thrust and unit cost are positively correlated (i.e., unit cost increases as average thrust increases). You have been provided the following sample data set regarding the

Statistics: RES 342
The data file contains information on 76 single-family homes in Eugene, Oregon during 2005. At the time the data were collected, the data submitter was preparing to place his house on the market and it was important to come up with a reasonable asking price. Whereas realtors use experience and local knowledge to subjectively v

Correlation and Regression
The coach of the Ottawa football team wants to determine if there is a relationship between how fast players can run 60 m and how far they can throw the football. The results for the Ottawa players were as follows: Player Spring Time (s) Throwing Distances (m) Jon H. 7.92 32 Tom M. 8.66 29 Sarjay P. 6.58 35 Brandon F. 8.

Scatter plot, correlation and regression
A study was done with a group of university students to determine if there was a correlation between the amounts of sleep they got and their academic performance. The following table lists some data from the study. Student A B C D E F G H I J K L Hours of Sleep 6.0 6.5 7.0 6.5 8.5 8.0,

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