Data Analytics using Regression Model

Suppose that a resource allocation decision is being faced whereby one must decide how many computer servers a service facility should purchase to optimize the firm’s costs of running the facility. The more servers they have, the less workers are needed. Too many servers will result in over-capacity and waste resources. The firm’s predictive analytics effort has shown a growth trend. A new facility is called for if costs can be minimized. The firm has a history of setting up large and small service facilities and has collected the 40 data points. Let’s consider the following linear model, and estimate that using the data.

Linear Model

Where COST = the total cost to maintain a service facility.

         X  = the number of servers installed in each service facility

Using the Excel data, copy and paste to MINITAB answer the following questions.

1) Estimate the model and copy and paste the results and explain the meanings of the estimated coefficients.
2) Find TSS, RSS, ESS and R square, and carefully explain their meanings.
3) Using t test, prove/disprove if the estimated coefficient b is significant
4) What are the elasticity of server on total cost if you have 20 servers, or 40 servers?

5) Let’s consider the following log linear model

Explain the coefficient of b and find the elasticity of number of server on the total cost.

6) Linear and Nonlinear Polynomial Models (1 point each)

a. Estimate the model and copy and paste the results and perform the F test for each model
b. Let’s compare the two models, the Linear vs. Nonlinear models. In terms of goodness-to-fit, which one fits better? Carefully explain.
c. According to each model, what are the total cost to maintain the facility if you want install 10, 20, 50 servers?
d. Choose the best model from the regression model in terms of goodness-to-fit, and find the number of servers to minimize the total cost of the service facility.

II. Single Family House Sales in Chicago
We obtain a house sales data from the local Multiple Listing Service (MLS) who provides the up-to-date real estate market listing prices. We obtain the following variables from the properties listed in Chicago in 2015.
BEDROOM : Number of Bedroom
BATHROOM : Number of Bathroom
SQFT : Square Feet of Living Area
GARAGE : Number of Cars in Garage
AGEBLD : Age of Building
FIREPLACE : Number of Fireplace
ZIP : Zip Code
PRICE : Listing Price

1. Find the descriptive statistics of Listing Price (PRICE) for two zip codes separately, and compare their central tendency, and variance using the following hypothesis tests: (1 points each)
2. Simple Regression Model (Estimate separate model for each zip code)
   Let’s consider the following simple regression model:
   
   1) Estimate the simple regression model, and copy and paste the results from Minitab Regression output from Minitab and explain the meaning of coefficients from each model. (1 point)

2) Using the simple regression output find the following statistics. (0.5 point each)
) Estimate the simple regression model, and copy and paste the results from Minitab Regression output from Minitab and explain the meaning of coefficients from each model. (1 point)

2) Using the simple regression output find the following statistics. (0.5 point each)

Statistics ZIP CODE 1 = ZIP CODE2 =
a. Estimated intercept
b. Estimated slope coefficient
c. Total Sum of Square (TSS)
d. Regression Sum of Square (RSS)
e. Error Sum of Square (ESS)
f. R2
g. Adjusted R2
h. Variance and standard error of b1
i. Correlation Coefficient between listing price (PRICE) and square feet (SQFT)
j. Variance of et

2. Nonlinear Model (Estimate separate model for each zip code, 1 point each)
   Let’s consider the following log transformed model.

1) Estimate the model and copy and paste the results, and explain the meanings of the estimated slope coefficients from each regression model.

2) Compare and explain the elasticity of square feet to price between two zip codes, which is

3. Multiple Regression Model (Estimate separate model for each zip code, 1 points each)

1) Estimate the model using Minitab, and copy and paste the results.
2) Explain the meanings of the estimated coefficients.
3) Perform the t tests to find which variables are significant. List all significant variables at 5% and 10% significance levels.
4) Perform the F test for the each regression model, explain your verdict from the test.
5) Let’s compare the simple regression and the multiple regression models for each zip code. Carefully explain which is better.

6) Challenging model (3 points)
Now let’s find the best model to explain the listing price using the given variables. Any combination or any different functional forms are allowed. Find the best possible model. After deciding your final model, justify why your model is better than the other models.

Dissertation Empirical Analysis Project

1. Plot the cross-sectional average of deposits/assets and Non-Deposit Debt/assets across time.

You can calculate Non-Deposit Debt = Assets – Deposits – Equity. How have the averages
evolved? How would you interpret your results?

2. Run OLS regressions of quarterly loan growth on non-deposit debt/assets (one quarter lagged value) controlling for bank size (i.e. one quarter lagged natural logarithm of total asset) and
   profitability (i.e. one quarter lagged return on assets) for the sub-sample of your data during the
   financial crisis (i.e. 2008Q1 – 2010Q1). You should have Bank and Time fixed effects in your
   regression. What is the sign and magnitude of the co-efficient on non-deposit debt/assets? Is the
   coefficient significant? How will you interpret the co-efficient? Justify your findings.
3. Compute two measures / (ex-post) proxies for bank risk
   a. Risk weighted asset divided by total assets
   b. Non-performing loans divided by total loans
4. Plot the cross-sectional average of the above two measures across time. How have the averages
   evolved across years? How would you interpret your results?
5. Run OLS regressions of the two ex-post measures of bank risk on equity over assets (one
   quarter lagged values). Control for bank size (i.e. one quarter lagged natural logarithm of total
   asset) and profitability (i.e. one quarter lagged return on assets) on the entire sample. You
   should have Bank and Time fixed effects in your regression. What is the sign and magnitude of
   the co-efficient on equity/assets? Is the coefficient significant? How will you interpret the coefficient? Justify your findings.
   Note: Make sure you winsorize all your variables (per quarter at the 1st and 99th percentile) to
   remove outliers.

How to calculate the probability of Hypergeometric Distribution

The expected value of Poisson distribution

Lesson Chapter 5 Review Questions

Qn1. Charity is planting trees along her driveway, and she has 6 pine trees and 6 willows to plant in one row. What is the probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other? Express your answer as a fraction or a decimal number rounded to four decimal places.
Q2. A person rolls a standard six-sided die 12 times. In how many ways can he get 6 fours, 5 ones, and 1 two?

Qn3. A card is drawn from a standard deck of 52 playing cards. What is the probability that the card will be a heart and not a seven? Express your answer as a fraction or a decimal number rounded to four decimal places.
Qn4. You are going to play mini golf. A ball machine that contains 21 green golf balls, 18 red golf balls, 23 blue golf balls, and 17 yellow golf balls, randomly gives you your ball. What is the probability that you end up with a blue golf ball? Express your answer as a simplified fraction or a decimal rounded to four decimal places.
Qn6.
A newspaper company classifies its customers by gender and location of residence. The research department has gathered data from a random sample of 1738
customers. The data is summarized in the table below.

Probability Distribution Table

What is the probability that a customer is female? Express your answer as a fraction or a decimal number rounded to four decimal places.

Qn7. A coin is tossed 3 times. What is the probability that the number of tails obtained will be 1? Express your answer as a fraction or a decimal number rounded to four decimal places.
Qn8. f a coin is tossed 5 times, and then a standard six-sided die is rolled 4 times, and finally a group of two cards are drawn from a standard deck of 52 cards without replacement, how many different outcomes are possible?

If a coin is tossed 5 times, and then a standard six-sided die is rolled 4 times, and finally a group of two cards are drawn from a standard deck of 52

cards without replacement, how many different outcomes are possible?

You can also solve this using technology.
Use The Fundamental Principle of Counting with the Combination Rule.
The experiments or tasks in this problem can be grouped into three basic types of activities, namely, tossing a coin 5
times, rolling a standard six-sided die 4
times, and drawing two cards from a deck of cards without replacement. To obtain the solution to the problem, the number of possible outcomes for each task is computed and then the Fundamental Principle of Counting is applied to the three tasks.
There are 25
outcomes possible when tossing a coin 5 times, 64 outcomes possible when rolling a standard six-sided die 4 times, and C252
outcomes possible when drawing two cards from a deck of cards without replacement. Applying the Fundamental Principle of Counting to these three tasks, we see that the total number of different outcomes possible is
25⋅64⋅C252=32⋅1296⋅1326=54991872
.Qn9.
6 cards are drawn from a standard deck without replacement. What is the probability that at least one of the cards drawn is a black card? Express your answer as a fraction or a decimal number rounded to four decimal places.
Qn11. In a history class there are 8 history majors and 8 non-history majors. 4 students are randomly selected to present a topic. What is the probability that at least 2 of the 4 students selected are non-history majors? Express your answer as a fraction or a decimal number rounded to four decimal places.
Qn12.
Jill is ordering pizza at a restaurant, and the server tells her that she can have up to three toppings: black olives, chicken, and spinach. Since she cannot decide how many of the toppings she wants, she tells the server to surprise her. If the server randomly chooses which toppings to add, what is the probability that Jill gets just spinach? Express your answer as a fraction or a decimal number rounded to four decimal places.

Qn13.
There are 77 students in a history class. The instructor must choose two students at random.
Academic Year History majors non-History majors
Freshmen 13 5
Sophomores 2 9
Juniors 12 12
Seniors 14 10
What is the probability that a junior non-History major and then another junior non-History major are chosen at random? Express your answer as a fraction or a decimal number rounded to four decimal places.

Qn14.
Customer account "numbers" for a certain company consist of 3 letters followed by 5 numbers.
Step 1 of 2 : How many different account numbers are possible if repetitions of letters and digits are allowed?
Qn15.
A coin is tossed 6 times. What is the probability that the number of heads obtained will be between 4 and 6 inclusive? Express your answer as a fraction or a decimal number rounded to four decimal places.
Qn16. A mail order company classifies its customers by gender and location of residence. The research department has gathered data from a random sample of 1936 customers. The data is summarized in the table below.

What is the probability that a customer lives in a dorm? Express your answer as a fraction or a decimal number rounded to four decimal places.

Qn18. A bag contains 9 red, 8 orange, and 7 green jellybeans. What is the probability of reaching into the bag and randomly withdrawing 16 jellybeans such that the number of red ones is 5, the number of orange ones is 7, and the number of green ones is 4? Express your answer as a fraction or a decimal number rounded to four decimal places.

Qn19.
Larissa is ordering apple pie at a restaurant, and the server tells her that she can have up to four toppings: walnuts, pecans, whipped cream, and caramel. Since she cannot decide how many of the toppings she wants, she tells the server to surprise her. If the server randomly chooses which toppings to add, what is the probability that Larissa gets just walnuts and pecans? Express your answer as a fraction or a decimal number rounded to four decimal places.