We are given a linear regression that gives us an equation on the relationship of Quantity on Total Cost. As stated in the project, the regression data is very good with a relatively high R2, significant F, and t-values but we can’t use this model to estimate plant size. When we perform a simple eye test on the residual plot for Q a trend seems to form from positive to negative and back to positive. When we also fit a linear trend line to the normal probability plot we can also see a pattern. This may indicate that the errors are not normally distributed; the effect is an increase in the tendency to reject the null hypothesis (type 1 error). But the easiest way to see that the model is not the best for this data is when you assign trend lines to the data.

Linear fit is ok, but you can see that the data is too spread out.

Polynomial to the 3rd order is a better fit, but we can do better.

Polynomial to the 2nd order is the best fit, the data is pretty “snug”.

Attached you will find the regression analysis for all three models with the 2nd order model having the best results with a high R2 and a very significant F with a better looking normal probability plot and Q/Q2 residuals distributed more randomly. The model that is produced with standard errors in parenthesis is: TC =| 347.9484| - 12.4285Q| + 0.356795Q2|

| (77.19129)| (5.50019)| (0.089795)|
| R2 = 0.7970| SEE = 58.9922| F = 52.9924|
| | | |

ATC =| 347.9484/Q| -12.4285| + 0.356795Q|
Both Q and Q2 are significant at an Alpha of .05 with the entire model being highly significant, if you conclude one or more of the coefficients is not equal to zero the probability of being wrong is less than 0.000000000449. This function is statistically better and can actually be used to estimate plant size.

...
Unit 5 – RegressionAnalysis
Mikeja R. Cherry
American InterContinental University
Abstract
In this brief, I will demonstrate selected perceptions of the company Nordstrom, Inc., a retailer that specializes in fashion apparel with over 12 million dollars in sales last year. I will research, review, and analyze perceptions of the company, create graphs to show qualitative and quantitative analysis, and provide a summary of my findings.
Introduction
Nordstrom, Inc. is a retailer that specializes in fashion apparel for men, women and kids that was founded in 1901. The company is headquartered in Seattle, Washington with over 61,000 employees world-wide as of February 2, 2013. (Business Wire, 2014)
Nordstrom, Inc. offers on online store, e-commerce, retail stores, mobile commerce and catalogs to its consumers. It operates 117 full-line stores within the United States and 1 store in Canada, 167 Nordstrom Rack stores, 1 clearance store under the Last Chance Banner, 1 philanthropic treasure & bond store called Trunk Club and 2 Jeffrey boutiques. The option of shopping online is also available at www.nordstrom.com along with an online private sale subsidiary Hautelook. They have warehouses, also called fulfillment centers, which manages majority of their shipping needs that are located in Cedar Rapids, Iowa. (Business Source Premier, 2014)
Nordstrom, Inc. continues to make investments in their e-commerce...

...REGRESSIONANALYSIS
Correlation only indicates the degree and direction of relationship between two variables. It does not, necessarily connote a cause-effect relationship. Even when there are grounds to believe the causal relationship exits, correlation does not tell us which variable is the cause and which, the effect. For example, the demand for a commodity and its price will generally be found to be correlated, but the question whether demand depends on price or vice-versa; will not be answered by correlation.
The dictionary meaning of the ‘regression’ is the act of the returning or going back. The term ‘regression’ was first used by Francis Galton in 1877 while studying the relationship between the heights of fathers and sons.
“Regression is the measure of the average relationship between two or more variables in terms of the original units of data.”
The line of regression is the line, which gives the best estimate to the values of one variable for any specific values of other variables.
For two variables on regressionanalysis, there are two regression lines. One line as the regression of x on y and other is for regression of y on x.
These two regression line show the average relationship between the two variables. The regression line of y on x gives the most probable...

...a 100β1 % change in Y.
(d) a 1% change in X is associated with a change in Y of 0.01β1 .
(iv) To decide whether Yi = β0 + β1 X + ui or ln(Yi ) = β0 + β1 X + ui fits the data better, you
cannot consult the regression R2 because
(a) ln(Y) may be negative for 0 < Y < 1.
(b) the TSS are not measured in the same units between the two models.
(c) the slope no longer indicates the effect of a unit change of X on Y in the log-linear
model.
(d) the regression R2 can be greater than one in the second model.
1
(v) The exponential function
(a) is the inverse of the natural logarithm function.
(b) does not play an important role in modeling nonlinear regressionfunctions in econometrics.
(c) can be written as exp(ex ).
(d) is ex , where e is 3.1415...
(vi) The following are properties of the logarithm function with the exception of
(a) ln(1/x) = −ln(x).
(b) ln(a + x) = ln(a) + ln(x).
(c) ln(ax) = ln(a) + ln(x).
(d) ln(xa) = aln(x).
(vii) In the log-log model, the slope coefficient indicates
(a) the effect that a unit change in X has on Y.
(b) the elasticity of Y with respect to X.
(c) ∆Y/∆X.
(d)
∆Y
∆X
×
Y
X
(viii) In the model ln(Yi ) = β0 + β1 Xi + ui , the elasticity of E(Y|X) with respect to X is
(a) β1 X
(b) β1
(c)
β1 X
β0 +β1 X
(d) Cannot be calculated because the function is non-linear
(ix) Consider the following least squares specification between testscores...

...RegressionAnalysis (Tom’s Used Mustangs)
Irving Campus
GM 533: Applied Managerial Statistics
04/19/2012
Memo
To:
From:
Date: April 19st, 2012
Re: Statistic Analysis on price settings
Various hypothesis tests were compared as well as several multiple regressions in order to identify the factors that would manipulate the selling price of Ford Mustangs. The data being used contains observations on 35 used Mustangs and 10 different characteristics.
The test hypothesis that price is dependent on whether the car is convertible is superior to the other hypothesis tests conducted. The analysis performed showed that the test hypothesis with the smallest P-value was favorable, convertible cars had the smallest P-value.
The data that is used in this regressionanalysis to find the proper equation model for the relationship between price, age and mileage is from the Bryant/Smith Case 7 Tom’s Used Mustangs. As described in the case, the used car sales are determined largely by Tom’s gut feeling to determine his asking prices.
The most effective hypothesis test that exhibits a relationship with the mean price is if the car is convertible. The RegressionAnalysis is conducted to see if there is any relationship between the price and mileage, color, owner and age and GT. After running several models with different independent...

...Quantitative Methods Project
RegressionAnalysis for the pricing of players in the
Indian Premier League
Executive Summary
The selling price of players at IPL auction is affected by more than one factor. Most of these factors affect each other and still others impact the selling price only indirectly. The challenge of performing a multipleregressionanalysis on more than 25 independent variables where a clear relationship cannot be obtained is to form the regression model as carefully as possible.
Of the various factors available we have leveraged SPSS software for running our regressionanalysis. One of the reasons for preferring SPSS over others was the ease with which we can eliminate extraneous independent variables. The two methodologies used for choosing the best model in this project are:
* Forward Model Building:
Independent variables in order of their significance are incrementally added to the model till we achieve the optimum model.
* Backward Elimination:
The complete set of independent variables is regressed and the least significant predictors are eliminated in order to arrive at the optimum model.
Our analysis has shown that the following variables are the most significant predictors of the selling price:
COUNTRY :...

...RegressionAnalysis Exercises
1- A farmer wanted to find the relationship between the amount of fertilizer used and the yield of corn. He selected seven acres of his land on which he used different amounts of fertilizer to grow corn. The following table gives the amount (in pounds) of fertilizer used and the yield (in bushels) of corn for each of the seven acres.
|Fertilizer Used |Yield of Corn |
|120 |138 |
|80 |112 |
|100 |129 |
|70 |96 |
|88 |119 |
|75 |104 |
|110 |134 |
a. With the amount of fertilizer used as an independent variable and yield of corn as a...

...l
RegressionAnalysis
Basic Concepts & Methodology
1. Introduction
Regressionanalysis is by far the most popular technique in business and economics for
seeking to explain variations in some quantity in terms of variations in other quantities, or to
develop forecasts of the future based on data from the past. For example, suppose we are
interested in the monthly sales of retail outlets across the UK. An initial dataanalysis would
summarise the variability in terms of a mean and standard deviation, but the variation from
outlet to outlet could be very large for a variety of reasons. The size of the local market, the
size of the shop, the level of competition, the level of advertising, etc.. would all influence the
sales volume from outlet to outlet. This is where regressionanalysis can be useful. A
regressionanalysis would seek to model the influence of these factors on the level of sales. In
statistical terms we would be seeking to regress the variation in sales ⎯ the dependent
variable ⎯ upon several explanatory variables such as advertising, size, etc..
From a forecasting point of view we can use regressionanalysis to develop predictions. If we
were asked to make a forecast for the monthly sales of a proposed new outlet in, say, Oxford,
we can simply compute the average outlet sales and put this...

...
Mortality Rates
RegressionAnalysis of Multiple Variables
Neil Bhatt
993569302
Sta 108 P. Burman
11 total pages
The question being posed in this experiment is to understand whether or not pollution has an impact on the mortality rate. Taking data from 60 cities (n=60) where the responsive variable Y = mortality rate per population of 100,000, whose variables include Education, Percent of the population that is nonwhite, percent of population that is deemed poor, the precipitation, the amount sulfur dioxide, and amount of nitrogen dioxide.
Data:
60 Standard Metropolitan Statistical Area (SMSA) in the United States, obtained for the years 1959-1961. [Source: GC McDonald and JS Ayers, “Some applications of the ‘Chernoff Faces’: a technique for graphically representing multivariate data”, in Graphical Representation of Multivariate Data, Academic Press, 1978.
Taking the data, we can construct a matrix plot of the data in order to take a visible look at whether a correlation seems to exist or not prior to calculations.
Data Distribution:
Scatter Plot Matrix
As one can observe there seems to be a cluster of data situated on what appears to be a correlation of relationship between Y=Mortality rate and X= potential variables influencing Y.
From this we construct a correlation matrix in order to see a relationship in matrix form....