SALES REPRESENTATIVE| NUMBER OF UNITS SOLD| NUMBER OF SALES CALLS| A| 28| 14|
B| 66| 35|
C| 38| 22|
D| 70| 29|
E| 22| 6|
F| 27| 15|
G| 28| 17|
H| 47| 20|
I| 14| 12|
J| 68| 29|
| | |
| | |

a) draw a scatter diagram of number of sales calls and number of units sold

b) Estimate a simple linear regression model to explain the relationship between number of sales calls and number of units sold y=2.139x-1.760
Number of units sold=2.139Number of units sold-1.760
c) Calculate and interpret the coefficient of correlation r=0.853=0.9236 (There is strong correlation between two variables as its near 1) d) the coefficient of determination
r2=0.853(The magnitude of the coefficient of determination indicates the proportion of variance in one variable, explained from knowledge of the second variable) e) the standard error of estimate

S.E=0.3133(The standard error is the estimated standard deviation of a statistic) f) Conduct a test of hypothesis to determine whether the coefficient of correlation in the population is zero H0:β1=0

Ha:β1≠0

t=β1SE =6.826
p-value for df=9 and t=6.826:0.001

0.0001<0.05
Therefore null hypothesis is rejected
Hence coefficient of correlation is zero is rejected
Therefore there is significant relationship between number of sales calls and number of units sold. g) Construct and interpret confidence intervals and prediction intervals for the dependent variable, number of units sold. Confidence interval:

(x-tsn,x+tsn)
Confidence interval for number of sales calls:

(x-tsn,x+tsn)
(0.924, 2.8612)

CALCULATIONS ON EXCEL

Regression Analysis| | | | | | |
| | | | | | | |
| r² | 0.853 | n | 10 | | | |
| r | 0.924 | k | 1 | | | |
| Std. Error | 8.412 | Dep. Var. | NUMBER OF UNITS SOLD| | | | | | | | | |
ANOVA table| | | | | | | |
Source| SS | df | MS| F| p-value...

...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...

...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 hypothesistests 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 testhypothesis that price is dependent on whether the car is convertible is superior to the other hypothesistests conducted. The analysis performed showed that the testhypothesis 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 hypothesistest that exhibits a relationship with the mean price is if the car is convertible. The RegressionAnalysis is conducted to see if there is...

...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 :...

...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 regression functions 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 and the studentteacher ratio:
TestScore = 557.8 + 36.42ln(Income).
According to this equation, a 1% increase income is associated with an increase in test
scores of
(a) 0.36...

...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....

...Chapter 9
RegressionAnalysis
1. a. Y = 250 + 3 X
b. Functional. For a given value of X there is one unique value of Y.
2. The model with the highest R2 might actually "overfit" the data and not provide accurate predictions. The R2 statistic can be inflated (or made arbitrarily large) by including superfluous independent variables in the model. If this happens the predictive ability of the model will actually be degraded since the model is biased toward sample specific anomalies in the data that may not be characteristic of the underlying population from which the sample was drawn.
3.
4. The solution would be unbounded. For virtually any regression problem, the sum of the estimation errors can be made to approach -¥ by selecting a regression function such that the estimated values a far greater than the actual values. Even in we place a lower bound of zero on the sum of the estimation errors, a regression function with a sum of estimation errors equal to zero will not necessarily fit the data well.
5. You should collect data so that the average value of the X1 observations is equal to X1h.
6. a. See file: Prb9_6.xls
There is a reasonably linear relationship between the variables -- except at the upper end of the X- axis. If possible we should investigate this anomaly in the data to make sure this is not due to a data entry error.
b. The estimated...

...
QoS Techniques: MPLS
CET 2486C – Network Technologies
Professor:
November 27, 2012
Abstract
MPLS or Multi Protocol Label Switching is a networking technology that functions between layers 2 and 3 of the OSI model. MPLS constitutes of adding a label (sometimes called “Shim” because of their placement between layer 3 and layer 2 headers.) to the data package, this label contains special addressing and sometimes prioritization information. Because the MPLS label contains all the information necessary for the router to forward the package to the next hop, the router does not have to spend time analyzing the entire package thus improving network latency or bottlenecks. Due to its multi protocol capabilities MPLS can be integrated with different networking technologies from ATM to native IP environments; in addition, this multi protocol capability also provides a way to converge different types of traffic such as data, voice and video onto one network. MPLS technology also provides some other advantageous features like Traffic Engineering (TE), VPN, Any Transport over MPLS (AToM) and Quality of Service (QoS). This paper will help provide an understanding of how MPLS works and the QoS capabilities it can provide.
History of MPLS
In 1996 a group from Ipsilon Networks introduced a “flow management protocol”, this technology only worked with ATM transmissions and did not become very popular in the market. Not long after Cisco...