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cluster coefficient

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You can see the notes that are attached. Please solve the following problems based on the notes.

1. Assume that the disutility of travel for consumers arrayed uniformly along a "Hotelling" line is not t as discussed in class, but t2, (i.e. the utility of a consumer for the product is:
Utility(Product i) = 3 - (ideal point - actual location product i)^2

There are two firms, A and B. The firms' locations are fixed and customers are uniformly distributed between the firms and the distance between the two firms is D. Each firm chooses a single price, PA and PB. Assume costs are zero.
A. What is the equation for the consumer at point X who is indifferent between the two firms?
B. What proportion of customers will buy from A and what proportion will buy from B?
C. What is firm A's profit function (as a function of prices and distance)?

2. You want to calculate the cluster coefficient for your own email contact list. That is, the set of names in your email address book is the relevant social network for your calculation.

A. Compose an email that you could send to each of these individuals asking for the data you would need to complete the calculation of the cluster coefficient.
Assume that:
Your friends have no idea what you are talking about, but they trust you and will provide you the data you ask for if you are clear about what you want.
You are not worried about maintaining the privacy of your email contact list or theirs.
You want to ask for the least amount of information as possible.

B. (Not necessarily in the email). Describe why if your friends comply this is enough data to compute the cluster coefficient.

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Solution Summary

Help is given to compute the cluster coefficient.

See Also This Related BrainMass Solution

Scatterplot, Correlation Coefficient, Linear Regression

See the attachments.

The regression equation and the standard error of estimate

Stewart Fleishman specializes in the psychiatric aspects of symptom management in cancer patients. Pain, depression, and fatigue can appear as single symptoms, in conjunction with one other symptom, or all together in patients with cancer. You are interested in testing a new kind of cognitive-behavioral therapy for the treatment of the simultaneous clustering of pain and fatigue in cancer patients. The following scores represent the decrease in symptom intensity (on a 10-point scale) following the new cognitive-behavioral therapy

Patient Pain (X) Fatigue (Y)
A 9 1.75
B 7 6.75
C 5 8
D 3 5.25
E 1 10

Create a scatter plot of these scores on the grid. For each of the five (X, Y) pairs, drag the orange points (square symbol) in the upper-right corner of the diagram to the appropriate location on the grid.

Calculate the means and complete the following table by calculating the deviations from the means for X and Y, the squares of the deviations, and the products of the deviations.

Scores Deviations Squared Deviations Products
X Y X-Mx Y-My (Y-Mx)^2 (Y-My)^2 (X-Mx)(Y-My)
9 1.75
7 6.75
5 8
3 5.25
1 10

Calculate the sum of the products and the sum of squares for X. SP = ______ and SSx = ______.

Find the regression line for predicting Y given X. The slope of the regression line is ______ and the Y intercept is ______.

Calculate the Pearson correlation coefficient, the predicted variability, and the unpredicted variability. The Pearson correlation is r = ______. The predicted variability is SSregression = ______. The unpredicted variability is SSresidual = ______

Calculate the standard error of the estimate. The standard error of the estimate is ______.

Suppose you want to predict the fatigue score for a new patient. The only information given is that this new patient is similar to patients A through E; therefore, your best guess for the new patient's level of fatigue is ______. The error associated with this guess (that is, the "standard" amount your guess will be away from the true value) is ______.
Suppose that now you are told the pain score for this new patient is 5.5. Now your best guess for the new patient's level of fatigue is ______. The error associated with this guess (that is, the "standard" amount your guess will be away from the true value) is ______.

Finally, suppose before estimating the regression equation, you first transform each of the original scores into a z-score. The regression equation you estimate is:
Z^y = ______ Zx

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