Question

Assume you have your own electricity bills for the last three years and that you have lived in the same house.

• Discuss how you could use bivariate regression to predict your upcoming electricity bills.

• Once you determine the statistically significant correlation and regression prediction, how much do you trust it?

• What would give you greater confidence to spend your savings on a vacation rather that keeping it in reserve for the electricity bill?

Answer 1

Bivariate regression uses 2 variables one is independent (predictor) variable and other is dependent(response) variable.

• To model this situation we can take amount of bill as dependent variable because we want to predict that and independent variable as no of hours spend at home.(assuming you live alone). Why I have taken number of hours spent at home? See when you are not at home some appliances would be working constantly and they will consume almost same electricity lile refrigerator. But when you are at home you might use TV , washing machine , dishwashers etc. So it would be a good choice to take number of hours as independent variable.
• We cannot put much confidence in our results even if we get significant correlation. Why? because there are less number of observations. for example assume you are on a career break so you spent much of your time at home so obviously you would be getting high costing bills so you might end up overestimating the amount. Similarly if you are on a trip due to work your monthly bills would cost less and you might end up underestimating.
• If we can have more observations i.e instead of 3 months if we can have 6 or 12 months electricity bill then we can have more confidence in our predictions and accordingly we can plan our spending on vacations. Also having more data will enable us to have a estimate of seasonal fluctuations so for example we know when there is not much heat consumption will be lower so we can plan our vacations at that time.  

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