Statistics Assignment on Forecasting
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The Excel file “CentralEnglandTemp2017” shows the 3216 monthly mean (surface air) temperatures for the Midlands region of England between 1750 and 2017. (The shown temperatures are in Celsius degrees measured with a precision of 0.1 °C.) The data set represents the longest reliable series of monthly temperature observations in existence, and hence is the most valuable source of information for meteorologists and climate scientists. It was originally published by Professor Gordon Manley in 1953, and has been subsequently updated until today.
It is quite obvious that the monthly temperatures for Midlands must have a seasonal pattern. However, the main purpose of the assignment is to examine the trend existence and its consequences.
1. Using XLMiner (Transform > Transform Categorical Data > Create Dummies), create 12 dummy variables corresponding to the 12 months (Jan, Feb,…,Dec). Since the categorical variable Month has 12 levels (categories), delete the dummy variable Jan; you will assume later the linear regression model with linear trend and seasonality:
Note. XLMiner shows the created dummy variables in the alphabetical order, so rename and rearrange them properly.
2. Create two separate data sets for the time periods 1750 – 1949 (2400 observations) and 1950-2017 (816 observations) on which you could run regression for the assumed regression model. For this purpose, you should create an additional independent variable t with values 1,2,…,2400 and 1,2,…,816, respectively.
3. Use the first data set (created for 1750-1949).
A. Run Regression (in Data Analysis of Excel or Multiple Regression in Predict of XLMiner) to find the estimated regression equation:
B. To verify the significance of the trend in the examined time series, test the hypotheses versus . What is the p-value of the test, the test conclusion and its interpretation? (Recall that in Excel, for example, 2E-08 is , which is practically zero.)
C. What is the interpretation of in the estimated regression equation? What is the estimated change in the average temperature over 100 years based on the 1750-1949 data? Note. Secure a sufficiently high accuracy in your calculations.
4. Use the second data set (created for 1950-2017).
A. Run Regression (in Data Analysis of Excel or Multiple Regression in Predict of XLMiner) to find the estimated regression equation:
B. To verify the significance of the trend in the examined time series, test the hypotheses versus . What is the p-value of the test, the test conclusion and its interpretation?
C. What is the estimated change in the average temperature over 100 years based on the 1950-2017 data? Compare this result with that found in Task 3C.
D. Using the estimated regression equation found in Task 4A, make forecasts for the first nine months of 2018. On the website www.metoffice.gov.uk/hadobs/hadcet/cet_info_mean.html, find the actual monthly temperatures (CET) recorded during the first nine months of 2018, and compare them with your forecasts by computing the nine forecast errors. How many times the actual temperature exceeds your forecasted temperature? How would you interpret your findings? Note. February and March of 2018 were exceptionally cold in the entire Western Europe. How this fact is reflected by the forecast errors.
E. In the regression model, assume the quadratic trend, that is,
After changing into in the data set, run Regression in Data Analysis of Excel or Multiple Regression in Predict of XLMiner to find the estimated regression equation:
F. Which of the two forecasting models (assumed in Tasks 4A and 4E) would you recommend and why?
5. Interpret your findings in light of the discussion about global warming. Feel free to express your opinion!
Note. You might be more accustomed to temperatures expressed in Fahrenheit degrees. If so, using the known formula: 0F = 9(0C)/5 + 32, you may convert all your 0C temperature data into 0F data.
Use Microsoft Word to write your answers. The Microsoft Word should include all relevant Excel/ XLMiner outputs (copy and paste them), and attach the Excel file that you work on it.
