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TABLE 5 <br />REGRESSION MODEL <br />Anal sis of Variance <br />Source DF S ua es S uare F Value Pr > F <br />Model 6 10.03204 1.67201 5.93 <.0001 <br />Error 160 4511980 0.28200 <br />Corrected <br />Total 166 5515185 <br /> Root MSE 0.53104 R-Square 0.1819 <br /> Dependent <br />Mean 5.24131 Adj R-Sq 0.1512 <br /> Coeff Var 10.13174 <br />Dependent Variable: Log gpcd <br />Parameter Estimates <br />Variable DF Parameter <br />Estimate Standard <br />Error t Value Pr > ~t~ <br />Interce t 1 4.98127 0.20381 24.44 <.0001 <br />Frontran e 1 -0.23713 0.09257 -2.56 0.0113 <br />Arkansas 1 -0.23934 0.09959 -2.40 0.0174 <br />SJ-Dolores 1 -0.42351 0.16263 -2.60 0.0101 <br />Rio Grande 1 0.28379 0.19049 1.49 0.1383 <br />Lo sfratio 1 -0.23430 0.12076 -1.94 0.0541 <br />Lo servratio 1 -0.25297 0.11925 -2.12 0.0354 <br />Table 6 shows the matrix of correlations between variables in the sample <br />data. Only those correlations with an acceptable statistical significance <br />(probability of 0.05 or less) are shown in the table. For example, data for the <br />maximum temperature in 2000 is significantly correlated with per capita <br />water use. The relationship is negative indicating that sample points with <br />lower maximum temperature tend to have higher per capita water use (a <br />relationship that is counter to what is expected). Also, maximum <br />temperature is significantly correlated with household income. Such a <br />relationship is referred to as a spurious correlation because there is no direct <br />causal relationship between the two variables. The explanation lies in the fact <br />that sample points with highest per capita water use are in the higher <br />elevations of the state with cooler maximum temperatures as are sample <br />points with the highest median household incomes. Conversely, sample <br />points with the lowest water use are in the south central and southeastern <br />part of the state and are associated with higher maximum temperatures and <br />lower incomes. Such spurious correlations among the explanatory variables <br />prohibit the regression analysis from discerning the relationship between <br />water use and the explanatory variables. (An underlying assumption of <br />regression analysis is that the explanatory variables are independent of one <br />another.) <br />16 IIL Data CollectionandAnalysis <br />