1. An Ice Cream shop owner wants to coordinate his stock levels with his sales. He believes he could forecast his sales based on the day’s temperature and whether it’s a weekend or not

1. An Ice Cream shop owner wants to coordinate his stock levels with his sales. He believes he could forecast his sales based on the day’s temperature and whether it’s a weekend or not. He collects data from 40 different days. The data is stored in Ice Cream.gdt
a) Graph the data using the appropriate graph (copy and paste it from gretl).
b) Use gretl to estimate a linear regression model to explain Ice Cream sales. Show your final results (copy and paste it from gretl)
c) Write your final estimated regression model.
d) Why is this the best model you came up with?
e) Graph the residuals from your final model; what do they say about your model?
f) Use your model to forecast ice cream sales if temperature is 28 degrees on a weekend.
g) Provide a 95% confidence interval of your forecast.

2. The Ministry of Economy is interested in building a model to explain consumption behavior among middle class households. It picks a sample of 35 households and collects data about their consumption, income, wealth, size, and age. The data is available in the file Consumption.gdt. The monetary data is in thousands of dollars.
a) Graph the data using the appropriate graph (copy and paste it from gretl).
b) Use gretl to estimate a linear regression model to explain Ice Cream sales. Show your final results (copy and paste it from gretl)
c) Write your final estimated regression model.
d) Why is this the best model you came up with? (Explain)
e) Diagnose the model for multicollinearity.
f) Graph the residuals from your model; what do they say about your model?
g) Use your model to forecast consumption for the following two family:
Family 1: Income (50), Wealth (10), Size (5), Age (46)
3. The file Morocco GDP.gdt contains data on Morocco’s Gross Domestic Product, agricultural value added, exports of goods and services, tourism receipts and remittances received from Moroccans living abroad.
a) Use the appropriate graph to represent the variables. (copy &paste it from gretl)
b) What should be done to these variables before we run a regression on them?
c) Estimate a linear regression model to explain Morocco’s GDP.
d) Are the coefficients significant? Drop any insignificant coefficients and re-estimate the model. Show your final results (copy and paste it from gretl)
e) Why is this the best model you came up with? (Explain)
f) Graph the residuals from your regression; what do they say about your model?

4. Google is the one of the most prominent companies listed in the NASDAQ. The Excel file below shows its daily price from January to April 2015.
a) Use the appropriate graph to represent the price of Google stock (copy & paste it from excel).
b) What type of pattern does the stock displays?
c) Use the different Sheets in the Excel file to run the following univariate models:
• Naïve
• 5-day moving average
d) Forecast the value of the stock in May 1st. (Save your work in the embedded Excel file)
e) Which of the two models is better at forecasting this time series? (use MSE)

5. The Excel file below contains data on total monthly tourist arrivals to Singapore from January 2009 to December 2014. As you could see from the time series plot, the data is seasonal.
a) Develop a Multiplicative Decomposition model (Y = TS + e) of the variable and use it to forecast tourist arrivals in each month of 2015. (Show all your work and save it in the embedded Excel file)
b) Evaluate your model using R² and Theil’s U-statistics.

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