ENG-156 HOMEWORKS

• Consider the California rainfall data available from the data sets page.
  • Use R to perform a full descriptive analysis of the available records including histograms and boxplots.
  • Define stations that have `high' altitude as those at more than 200 feet of altitude and `far' stations as those which are more than 70 miles away from the coast. Compare the average rainfall of `hig' and `low' stations and of `far' and `close' ones.
  • Consider the four groups that are produced by jointly taking the `far' and `high' classification. Compare the distributions of those groups. Produce a plot that contains the boxplots of the data by group.
  • Explore the influence of the latitude on the rainfall. Will it make sense to group the stations in terms of this variable?
• Problems 3.8; 3.16; 3.26; 3.62; 3.71 of the textbook.
• Back to the California rainfall data.
  • Fit a simple linear regression to the rainfall using the latitude as an explanatory variable. Plot the result.
  • Create a vector od 0s and 1s corresponding to the `high' and not `high' stations. Fit a regression model that considers different slopes and intercepts for those two groups, with latitude as the regressor. Plot your fit using different colours for each group of data and fitted lines. Are the lines significantly different?
  • Repeat the previous analysis for the `far' grouping of the data.
  • Fit a linear model with all three covariates: latitude, distance and altitude. Are the results consistent with your previous analyses?
• Problems 4.19; 4.23; 4.28; 4.42; 4.43
• Problems 4.48 and 4.49 using the coefficient of determination, the adjusted coefficient of determination, AIC and BIC. The data are available from the data sets web page.
• Consider the data of eample 5.3 in the textbook. Fit a full second order surface and estimate the optimal levels of temperature and pressure. Obtain a 95% predictive interval for the quality that corresponds to the estimate optimal combination. The data are available from the data set web page.
• Problems 5.21; 5.27
• Back to the California rainfall data. Read chapter 13 and perform the analysis suggested in it. Problems 13.1 and 13.2.
• Problem 7.21. The data are available from the data web page.