Problem 1

  1. Plot data on map under different projections.

  1. Regression model for temperature data. The coordinates are centered before fitting the model.

From the ANOVA table, both variables are very sigificant. The model adjusted \(R^2\) is 0.9419, that shows most of the variability of the temprature is explained by the model.

There are no obvious pattern in the residual vs fitted value plot. That indicates the errors are independent. The residual is quite normal and no obvious influential points. The residual is plotted onto a map. We can see large residual are all on the edge of the spatial domain.

  1. A grid in the range of the data is produced. The model is applied to the centered grid and the prediction value is calculated. However, the grid is transformed back to its original scale to obtain the plots.

Problem 2

There are some cluster effect on the map: The income level in neighboring counties are clustered. This may be further explained by other geographical variables like height or if there is metropolitan city in the area.

Problem 3

The data is from a facility registry system (FRS) in Conniticut. The FRS contains accurate and authoritative facility identification records which are subjected to rigorous verification and data management quality assurance procedures. The geospatial location of the facility site (i.e., latitude/longitude and method, accuracy, and description data) is used to plot the data onto the following map.