1. There are three objects being added to the workspace. They are boston.c, a data.frame of 506 observations and 20 variables, boston.utm, a matrix of tract point coordinates projected to UTM zone 19 is included as boston.utm, and a sphere of influence neighbours list as boston.soi.

  2. Both Moran’s I test and Geary’s C test have p-value \(< 2.2e-16\). The test statistic are \(I = 0.764378416\) and \(C = 0.236626006\). Both assumed normality of the test statistic.

  3. The results of the OLS estimates are in the following table. The variables are CRIM: crime per capita; ZN: a numeric vector of proportions of residential land zoned for lots over 25000 sq. ft per town (constant for all Boston tracts); INDUS: proportions of non-retail business acres per town (constant for all Boston tracts); CHAS: a factor with levels 1 if tract borders Charles River; 0 otherwise; AGE: proportions of owner-occupied units built prior to 1940; PTRATIO: pupil-teacher ratios per town (constant for all Boston tracts).

    E stimate Std . Error t value Pr (>|t|)
    (Intercept) 4.3173005 0.1343578 32.1328507 0.0000000
    CRIM -0.0140972 0.0016886 -8.3485585 0.0000000
    ZN -0.0000405 0.0007239 -0.0558889 0.9554526
    INDUS -0.0141502 0.0026855 -5.2691300 0.0000002
    CHAS1 0.2178128 0.0516889 4.2139206 0.0000298
    AGE -0.0019925 0.0006495 -3.0679063 0.0022728
    PTRATIO -0.0515958 0.0068329 -7.5511312 0.0000000

We can see that CRIM, INDUS, CHAS1, AGE, and PREATIO are significant, but ZN is not.

Another model using the corrected median house dependent variable is slightly better than the first one. The Adjusted R-square is \(0.5005\) comparing to \(0.4992\) in model 1. The residual standard error is \(0.2886\) comparing to \(0.2893\) before and The AIC is \(187.1498\) comparing to \(189.6171\).

Regression diagnostics for model 2

  1. The Moran’s I statistic on residuals is \(0.4364296993\) with p-value \(< 2.2e-16\).