STATS302 Assignment 3 Questions

Jones The datafile “comfortable.csv” has average daily electricity consumption profiles for 640 households. These households were part of a study as to whether different pricing structures would influence power consumption patterns. There are two different tariff types: “Standard,” where pricing is constant, and “Time of Use” where the price depends on demand at a particular time (with that demand information provided to the consumer).

Q1. Make a boxplot of the log(usage) usage at each timeperiod under the Time of Use tarrif (ToU) and anotherunder the Standard tarrif (Std.), constraining the axes to have the same limits. Perform a test for a differencein consumption for each of the 48 time periods separately. Do any of the tests have p-value < 0.05? If so,what timeperiod does it correspond to? How do you interpet this, considering the number of tests performed?

Q2. Use a multivariate Levene’s test to test whether the covariances of log(usage) within the two groups are equal.

Q3. For the log(usage) data, compute the Mahalanobis distance of each point to to the group centers. Does thishave a Chi-squared distribution with 48 degrees of freedom? Use both a test and a visual assessment via aqq-plot. What do you conclude about the multivariate normality of the data?

Q4. Compute p-values both for a parametric manova, and for one based on residual resampling. Which do youprefer? Explain why. What are the conclusions from your preferred test?

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