The BBC website
www.bbc.co.uk/weather has average monthly statistics about the weather in at least one location for each country. I have downloaded some of this data for you to analyse. To situate the problem, perhaps imagine you run a travel agency. You wish to build a model that predicts, from basic weather statistics, the heat / humidity discomfort for other locations not included in the BBC’s database. By all means try other alternatives to those I am about to suggest, but unless they are better, I don’t want to know.
Step 1. First, this model is about discomfort from heat and humidity. We therefore surely don’t need to consider months in which it freezes, or even is relatively mild! To do so will only force the regression equation to explain stuff that doesn’t need explanation. On the other hand, we do need some months classified as zero in our data. But these should be the kinds of months that are warm, but not cold. I suggest you only include months that have temperatures greater than 18 degrees C. An alternative is to use the variables filterHH1month or filterHH2months to select only those months that are close to discomfort months. Use SPSS’s DATA / SELECT CASES / IF… / maxtemp>18. Here, I presume you have a variable in SPSS called MaxTemp.
Model 1. Regress Discomfort Rating on (1) Average Max Temp, (2) Humidity (am), (3) WetDays, (4) Sunlight. Tell me what you find and why you think you find it.
Model 2. Now add the interaction term of Average Max Temperatre with Humidity. Does this term add significant explanatory power to Model 1? Use the F for Change in R2 to test it. What has happened to the coefficients on the variables and why?
Models 1a & 2a. Repeat Model 1 and Model 2, but using mean centred versions of MaxTemp and Humidity. Show me that the corresponding regression are equivalent. Now interpret the cofficients, in particular the nature of the interaction.
Model 3. Add dummy variables for location. If this results in a significant Change in R2, presumably there are factors that make different locations more / less uncomfortable than Model 2a predicts. What kinds of factors could these be?
Use Model 2a to predict the level of discomfort for a month in which
Average Max temperature = 30
Humidity = 80
Average Number of Wet Days = 10
Average Hours of Sunlight = 5.
Give me the answer both as a Number, and as a Word (e.g. Moderate). Tell me how you get the word from the number. Finally, check whether the regression assumptions have been met, suggest limitations of the model and possible improvements to it.
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