Question

The weather company you work for is performing an analysis on predicting sandstorms accurately in Phoenix. You have been given a large dataset and are asked to determine which factors could be used to accurately predict them.

The dataset you are provided with has over 50 variables. With your vast knowledge of Excel, you determine that 4 variables can be used as predictors to accurately predict sandstorms. Your boss is not convinced and decided to ask you some questions.

1. You mentioned that before you even begin doing this “regression analysis” of yours, you discarded about half of the variables. How did you choose which variables to discard, and more importantly, why does it matter?

2. You asked a friend and he told you that in his company they use both “Relative Humidity” and “Number of Sunny Hours” to predict sandstorms. In your report, you mention you only use the “Relative Humidity”, because of it being highly correlated with “Number of Sunny Hours”.  However, by themselves each are good predictors, why didn’t you use both? Wouldn’t that make the model better?

3. By looking at the correlation matrix you created between independent variables and the dependent variable, which independent variables based on the type of correlation did you discard or keep, and why?
   1. Strong positive correlation
   2. Weak positive correlation
   3. No correlation
   4. Weak negative correlation
   5. Strong negative correlation

Answer 1

A. Predictor variables can be excluded from the analysis on the basis of the following:

Identify outliers and influential points - maybe exclude them at least temporarily.

The need to keep only the required predictor variables in the regression analysis because of the following reasons:

1)  Unnecessary predictors will add noise to the estimation of other quantities that we are interested in. Degrees of freedom will be wasted

2) Collinearity is caused by having too many variables trying to do the same job.

3) If the model is to be used for prediction, we can save time and/or money by not measuring redundant predictors.

B. As both “Relative Humidity” and “Number of Sunny Hours” are highly correlated, it will add collinearity in the model as both the variables are doing the same job.

C. the variables to keep or discard will depend on the interest of your output. We cannot filter the correlation values. If there is a correlation between independent and dependent variables, those will be included in the analysis. If dependent and independent variables do not have any correlation, that variables will be excluded from the analysis. Hence, the variables with the following types of correlation will be included in the analysis:

1. Strong positive correlation
2. Weak positive correlation
3. Weak negative correlation
4. Strong negative correlation

variables with no correlation will be excluded from the analysis.