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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.

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. 

Linear Model Project for County Data

Analysis of county data: find the line of best fit, plot the data and the line, interpret the slope, and use the linear equation to make a prediction. Also, find r2 (coefficient of determination) and r (correlation coefficient). Data and list of tasks attached.

Marketing Consulting Firm

Complete Microsoft Excel problems "Computer Exercise 2 and 3" in the attachment. Please show your work in Microsoft Excel.

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 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?

Would simple linear regression analysis be the appropriate forecasting technique?

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

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 minimizes f(β). (This valu

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: ï" x =134, ï" y = 410, ï" x2 =3 020, ï"y2=24000, and ï" xy =8340. Estimate the linear regressi

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

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.


3. Nine different students were given version A of a test designed to measure their critical thinking skills. The students then took a course in critical thinking. At the end of the course the students took version B of the same test. You are asked to determine if the course was effective in improving their scores. Student

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

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


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.


12.48 In the following regression, X = weekly pay, Y = income tax withheld, and n = 35 McDonaldâ??s employees. (a) Write the fitted regression equation. (b) State the degrees of freedom for a two tailed test for zero slope, and use Appendix D to find the critical value at ? = .05. (c) What is your conclusion about the slope? (d

Multiple Regression Analysis

For this case we are going to look at housing starts again, but this time we are going to add another variable to the equation. The historical values below give interest rates, lumber prices (dollars per board-foot) and number of starts. We will compute a multiple regression equation using these variables, with starts as the D

Regression Analysis

For this case, we will examine some hypothetical data concerning interest rates and the number of housing starts per month. A new "housing start" is counted when a contractor begins construction of a new private house. Create a scatterplot with interest rates on the X-axis and the number of housing starts on the Y-axis. (Fo

Correlation and Regression Analysis

1. A sample of 12 homes sold last week in St. Paul, Minnesota, is selected (see table below). Size of Home('000 Sq. Ft) Selling Price ($'000) 1.4 100 1.3 110 1.2 105 1.1 120 1.4 80 1.0 105 1.3 110 0.8 85 1.2 105 0.9 75 1.1 70 1.1 95 A) If we want to estimate selling price based on the size of home, which va

Linear Regression

What is the idea behind linear regression? What is it? Why do it? What are some limitations of linear regression?

Correlation & Regression: Number of lunches sold and Price

The fast food restaurant "FRIED CHICKEN POPEYE" periodically offers lunches that include three pieces of chicken, chips, soda and desserts can be eaten in the restaurant or take it elsewhere, special prices. Let Y be the number of lunches sold and X the price. Based on historical observations and calculations in the table below,

Least Squares Regression Line and MAD

For the data below Year Automobile Sales Year Automobile Sales 1990 116 1977 119 1991 105 1998 34 1992 29 1999 34 1993 59 2000 48 1994 108 2001 53 1995 94 2002 65 1996 27 2003 111 (a) Determine the least squares regression line. (b) Determine the predicted value for 2004. (c) Determine the MAD. (d) Determine th

Simple linear regression

Simple Linear Regression -- Sales "A recent study was conducted to determine the relation between advertising expenditures and sales of widgets for the first year of production. " You would like to determine the effect of your ad expenditures in predicting sales. the following data was colle

Functions, Graphs, and Models

Assistance to use algebraic and graphing concepts to solve problems involving real data. Exercise 1.3 39. Internet Recruiting The percentage of fortune Global 500 firms that actively recruited workers on the internet from 1998 through 2000 can be modeled by P(x) = 26.5x - 194.5 percent, where x is the numb