Continental Airlines (CA) is reluctant to begin service at the new Delayed Indefinitely Airport (DIA) until the automated baggage-handling system can transport luggage to the correct location with at least 99% reliability for any given flight. Lower reliability will result in damage to CA’s reputation for quality service. The baggage system will not deliver to the right location if any of its subsystems fail. The subsystems and their reliability for satisfactory performance during operation for any given flight are shown in the following table.

subsystemreliability
Power Supply70.0% surge free
Scanner reading99.8% accurate
Computer software98.2% glitch free
Mechanical systems97.5% jam free
Operators96.0% error free

a. What is the reliability of the luggage system for any given flight?

b. Installing surge protectors increases power supply reliability to 99.9%. What is the reliability of the new luggage system?

Problem 6.5

The manager of Perrotti’s Pizza collects data concerning customer complaints about delivery. Pizza is arriving late, or the wrong pizza is being delivered.

problemfrequency
Topping stuck to box lid17
Pizza is late35
Wrong topping or combination9
Wrong style of crust6
Wrong size4
Pizza is partially eaten3
Pizza never showed up6

a. Use a Pareto chart to identify the “few vital” delivery problems.

b. Use a cause-and-effect diagram to identify potential causes of late pizza delivery. Problem 7.4

The Canine Gourmet Company produces delicious dog treats for canines with discriminating tastes. Management wants the box-filling line to be set so that the process average weight per packet is 45 grams. To make sure that the process is in control, an inspector at the end of the filling line periodically selects a random box of ten packets and weighs each packet. When the process is in control, the range in the weight of each sample has...

...Regression Analysis: A Complete Example
This section works out an example that includes all the topics we have discussed so far in this chapter.
A complete example of regression analysis.
PhotoDisc, Inc./Getty Images
A random sample of eight drivers insured with a company and having similar auto insurance policies was selected. The following table lists their driving experiences (in years) and monthly auto insurance premiums.
Driving Experience (years) Monthly Auto Insurance Premium
5 2 12 9 15 6 25 16
$64 87 50 71 44 56 42 60
a. Does the insurance premium depend on the driving experience or does the driving experience depend on the insurance premium? Do you expect a positive or a negative relationship between these two variables? b. Compute SSxx, SSyy, and SSxy. c. Find the least squares regression line by choosing appropriate dependent and independent variables based on your answer in part a. d. Interpret the meaning of the values of a and b calculated in part c. e. Plot the scatter diagram and the regression line. f. Calculate r and r2 and explain what they mean. g. Predict the monthly auto insurance premium for a driver with 10 years of driving experience. h. Compute the standard deviation of errors. i. Construct a 90% confidence interval for B. j. Test at the 5% significance level whether B is negative. k. Using α = .05, test whether ρ is different from zero.
Solution a. Based on theory and intuition, we...

...Determinants of Production and Consumptions
Determinants of Industry Production (Supply)
Supply is the amount of output of production that producers are willing and able to sell at a given price all other factors being held constant.
The following are the determinants of supply:
Price (P), Numbers of Producers (NP), Taxes (T)
Model Specification
Specification of model is to specify the form of equation, or regression relation that indicates the relationship between the independent variables and the dependent variables. Normally the specific functional form of the regression relation to be estimated is chosen to depict the true supply relationships as closely possible.
The table presented below gives the hypothetical quantity supplied for a particular product (Qs) of a particular place given its price per kilo (P/kl), the Numbers of producers (NP), and tax per kilo (T/kl) for the period 2002 to 2011. (The quantity Supplied is expressed as kilo in millions)
Table
|Year |Qs |P/kl |NP |T/kl |
|2002 |21.4 |23 |39 |1.15 |
|2003 |23.9 |25 |41 |1.25 |
|2004...

...associated with a β1 change in Y.
(iii) The interpretation of the slope coefficient in the model ln(Yi ) = β0 + β1 ln(Xi ) + ui is as
follows:
(a) a 1% change in X is associated with a β1 % change in Y.
(b) a change in X by one unit is associated with a β1 change in Y.
(c) a change in X by one unit is associated with 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 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...

...Regression Analysis 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 dependent...

...Linear-Regression Analysis
Introduction
Whitner Autoplex located in Raytown, Missouri, is one of the AutoUSA dealerships. Whitner Autoplex includes Pontiac, GMC, and Buick franchises as well as a BMW store. Using data found on the AutoUSA website, Team D will use Linear Regression Analysis to determine whether the purchase price of a vehicle purchased from Whitner Autoplex increases as the age of the consumer purchasing the vehicle increases. The data set provided information about the purchasing price of 80 domestic and imported automobiles at Whitner Autoplex as well as the age of the consumers purchasing the vehicles. Team D selected the first 30 of the sampled domestic vehicles to use for this test. The business research question Team D will answer is: Does the purchase price of a consumer increase as the age of the consumer increases? Team D will use a linear-regression analysis to test the age of the consumers and the prices of the vehicles.
Five Step Hypothesis Testing
Team D will conduct the two-sample hypothesis using the following five steps:
1. Formulate the hypothesis
2. State the decision rule
3. Calculate the Test Statistic
4. Make the decision
5. Interpret the results
Step 1- Formulate the Hypothesis
Using the research question: Does the purchase price of an automobile purchased at Whitner Autoplex, increase as the age of the consumer purchasing the vehicle...

...Regression Analysis (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 regression analysis 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 Regression Analysis 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 variables, it is concluded that there is a relationship between the price and...

...
A. DETERMINE IF BLOOD FLOW CAN PREDICT ARTIRIAL OXYGEN.
1. Always start with scatter plot to see if the data is linear (i.e. if the relationship between y and x is linear). Next perform residual analysis and test for violation of assumptions. (Let y = arterial oxygen and x = blood flow).
twoway (scatter y x) (lfit y x)
regress y x
rvpplot x
2. Since regression diagnostics failed, we transform our data.
Ratio transformation was used to generate the dependent variable and reciprocal transformation was used to generate the independent variable.
3. Check if the model is adequate by checking the t-statistic, R2 and F-statistic.
F statistic reveals that the equation used to determine the relationship between the x and y is functional. Using the test statistic for the test of coefficients, it was revealed that the constant value in the equation is not significantly different from 0. Also, it was revealed that the transformed x, significantly explains the dependent variable. Also, it was revealed that the measure of proportion of variability explained by the fitted value is relatively high with 96.23%. This means that transformed data in blood flow explains 96.23% of the variation in the transformed data in arterial oxygen.
4. Check the normality of residuals and equal variances
predict r, resid
kdensity r, normal
pnorm tx
qnorm tx
rvpplot tx
Before we could perform the numerical test, we must first generate the r by the...

...REGRESSION ANALYSIS
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 regression analysis, 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 value of y for given value of...