Business Finance - Economics Business Statistic Lab Assignment

Project-3

QBA775- Quantitative Methods

Due-04-16-2023 at 11:59 PM

• You can discuss this lab-work with any other student in the class.

• You can get help or clarification from the instructor.

• You are permitted to use the course notes, books, the internet, Rscript posted on blackboard,

and any other materials you like.

• For each question, you need to fully interpret your results. Your report should be typed. You

should include your code as an appendix and cite your output properly.

• You can upload your lab-work file under lab assignment folder in Blackboard.

• Late submission is not accepted.

• Project-3’s data are available under Data folder.

• Use of RStudio is required for all project in this class.

1. [25 pts] Imagine that you have been asked to join the team supporting a young New York

City chef who plans to create a new Italian restaurant in Manhattan. The stated aims of the

restaurant are to provide the highest quality Italian food utilizing state-of-the art decor while

setting a new standard for high-quality service in Manhattan. The creation and the initial

operation of the restaurant will be the basis of a reality TV show for the US and international

markets (Including Australia). You have been told that the restaurant is going to be located

no further south than the Flatiron District and it will be either east or west of Fifth Avenue.

You have been asked to determine the pricing of the restaurants dinner menu such that

it is competitively positioned with other high-end Italian restaurants in the target area. In

particular, your role in the team is to analyze the pricing data that have been collected in

order to produce a regression model to predict the price of dinner. Actual data from surveys

of customers of 168 Italian restaurants in the target area are available. The data are in the

form of the average of customer views on. Use Nyc.xls data

Y = Price = The price (in $US) of dinner (including one drink and a tip)

x1 = Food = customer rating of food (out of 30)

x2 = Decor = Customer rating of the decor (out of 30)

x3 = Service = customer rating of the service (out of 30)

x4 = East = dummy variable = 1(0) if the restaurant is east(west) of Fifth Avenue.

1

In particular you have been asked to

(a) [5 pts] Develop a regression model that directly predicts the price of dinner ( in dollars)

using a subset or all of four potential predictor variables listed above.

(b) [5 pts] Determine which of the predictor variables Food, Decor and Service has the

largest estimated effect on price? Is this effect also the most statistically significant.

(c) [5 pts] If the aim is to choose the location of the restaurant so that the price achieved for

dinner is maximized, should the new restaurant be on the east or west of Fifth Avenue?

(d) [5 pts] Does it seems possible to achieve a price premium for ” setting a new standard

for high-quality service in Manhattan” for Italian restaurants?

(e) [5 pts] Identify the restaurants in the data set which, given the customer rating, are

usually (1) unusually highly priced; and (ii) unusually lowly priced.

2. [40 pts]Nuclear power Here are data on 32 light water nuclear power plants. The variables

are:

Cost: In $100,00, adjusted to 1976 base.

Date: date that construction permit was issued in years after 1900. Thus, 68.58 is roughly

halfway through 1968

Mwatts: Power plant net capacity in megawatts

We are interested in the Cost of the plants as a function of date and Mwatts. Use Nucle-

arpower.xls data

(a) [5 pts] Examine the relationship between Cost and Mwatts and between cost and Date,

Make appropriate display and interpret them with a sentence or two.

(b) [5 pts] Find the regression of Cost on Mwatts. Write a sentence that explains the

relationship as described by the regression.

(c) [5 pts] Make a scatterplot of residuals vs. predicted values and discuss what it shows.

Make a Normal probability plot of histogram of the residuals. discuss the four assump-

tion needed for regression analysis and indicate whether you think they are satisfied

here. Give your reasons.

(d) [5 pts] State the standard null hypothesis for the slope coefficient and complete the t-test

at the 5% level. state your conclusion.

(e) [5 pts] Estimate the cost of 1000-mwatt plant. Show your work.

(f) [5 pts]. Discuss the meaning of r-squared in this regression. Plot the residuals against

date. Does it appear that date can account for some of the remaining variability?

(g) [5 pts] Compute the multiple regression of Cost on both Mwatts and date. Compare the

coefficient in this regression with those you have found for each of these predictors.

(h) [5 pts] Would you expect Mwatts and Date to be correlated?Why or why not? Examine

the relationship between Mwatts and date. Make a scatterplot and find the correlation

coefficient, for example. it’s only because of the extraordinary nature of this relationship

that the relationship you saw at earlier steps were this simple.

2

3. [40 pts] Alumni donations are an important source of revenue for colleges and universities.

If administrators could determine the factors that could lead to increases in the percentage

of alumni who make a donation, they might be able to implement policies that could lead to

increased revenues. Research shows that students who are more satisfied with their contact

with teachers are more likely to graduate. As a result, one might suspect that smaller class

sizes and lower student/faculty ratios might lead to a higher percentage of satisfied graduates,

which in turn might lead to increases in the percentage of alumni who make a donation. Use

data alumnigiving.xls

Table 1: Variable Descriptions

Variable Descriptions

Name Name of the college or university State State where the college or university is located

Graduation Rate Percentage of students who initially enrolled and graduated % of Classes Under 20 Percentage of classes with fewer than 20 students

Student/Faculty Ratio Number of students enrolled divided by the total number of faculty Alumni Giving Rate Percentage of alumni who donate to the college or university

Analysis and Managerial Report:

(a) [5 pts]Use methods of descriptive statistics to summarize the data.

(b) [5 pts] Develop an estimated simple linear regression model that can be used to predict

the alumni giving rate, given the graduation rate. Discuss your findings.

(c) [5 pts] Develop an estimated multiple linear regression model that could be used to

predict the alumni giving rate using Graduation Rate, % of Classes Under 20, and

Student/Faculty Ratio as independent variables. Discuss your findings.

(d) [5 pts] Based on the results in parts (b) and (c), do you believe another regression model

may be more appropriate? Estimate this model, and discuss your results.

(e) [10 pts] Interpret results

i. What conclusions and recommendations can you derive from your analysis?

ii. What universities are achieving a substantially higher alumni giving rate than

would be expected, given their Graduation Rate, % of Classes Under 20, and Stu-

dent/Faculty Ratio?

iii. What universities are achieving a substantially lower alumni giving rate than would

be expected, given their Graduation Rate, % of Classes Under 20, and Student/Faculty

Ratio?

iv. [5 pts] What other independent variables could be included in the model?

(f) [5 pts] Summarize and discuss as presenting to the executive management team

3

4. [30 pts] The file lab-3.xlsx contain data on 150 homes that were sold recently in a particular

community.

(a) [10 pts] Find a table of correlation between all of the variables. Do the correlation

between Price and each of the other variables have the sign(positive or negative) you

would expect? Explain briefly.

(b) [10 pts]Run a regression of Price versus rooms. What does the 95% confidence level

for the coefficient of Rooms tell you about the effect of Rooms on Price for the entire

population of such homes?

(c) [10 pts] Run a multiple regression of price versus Home Size, Lot Size, Rooms, and

Bathrooms. What is the 95% confidence interval for the coefficient of Rooms now? Why

you think it can be so different from the one in part (b)? Based on this regression, can

you reject the null hypothesis that the population regression coefficient of room is zero

versus a two-tailed alternative? What does this mean?

5. [30 pts] Forecasting Food and Beverage Sales The Vintage Restaurant, on Captiva Is-

land near Fort Myers, Florida, is owned and operated by Karen Payne. The restaurant just

completed its third year of operation. During those three years, Karen sought to establish a

reputation for the restaurant as a high-quality dining establishment that specializes in fresh

seafood. Through the efforts of Karen and her staff, her restaurant has become one of the

best and fastest-growing restaurants on the Island.

To better plan for future growth of the restaurant, Karen needs to develop a system that

will enable her to forecast food and beverage sales by month for up to one year in advance.

The data set (vintage.xls) shows the value of food and beverage sales ($1,000s) for the first

three years of operation:

Managerial Report

Perform an analysis of the sales data for the Vintage Restaurant. Prepare a report for Karen

that summarizes your findings, forecasts, and recommendations. Include the following:

(a) [10 pts] A time series plot. Comment on the underlying pattern in the time series.

(b) [20 pts] Using the dummy variable approach, forecast sales for January through Decem-

ber of the fourth year. How would you explain this model to Karen?

Assume that January sales for the fourth year turn out to be $295,000. What was your

forecast error? If this error is large, Karen may be puzzled about the difference between your

forecast and the actual sales value. What can you do to resolve her uncertainty about the

forecasting procedure?

4