The model above contains no direct effects between trust and spending.per.cap, yet there is a correlation between these variables as above (in Question 3). Explain how the model attempts to account for this correlation. (Hint: there is an important word that I will be looking for in your answer to this question.)

Data and information to answer the question above:

Question 3: What correlation does R report between: trust and ineq10; and between trust and spending.per.cap and how would you interpret both these correlations?

Correlation between trust and ineq10: -0.4534901 Correlation between trust and spending.per.cap: 0.5375404

data:

> gdp.thousands.per.cap <- gdp.per.cap / 1000 > print (mean(gdp.per.cap)) [1] 36831.03 > print (mean(gdp.thousands.per.cap)) [1] 36.83103 > > spending.per.cap <- spend.per.cap / 1000 > print (mean(spend.per.cap)) [1] 7648.308 > print (mean(spending.per.cap)) [1] 7.648308 > > print (mean(trust)) [1] 34.43824 > print (mean(ineq10)) [1] 9.461765 > > print (var(gdp.thousands.per.cap)) [1] 201.0941 > print (var(ineq10)) [1] 29.33092 > print (var(spending.per.cap)) [1] 13.91994 > print (var(trust)) [1] 241.3758 > > print (var(gdp.thousands.per.cap)^0.5) [1] 14.18077 > print (var(ineq10)^0.5) [1] 5.415803 > print (var(spending.per.cap)^0.5) [1] 3.730943 > print (var(trust)^0.5) [1] 15.53627 > > print (cov(ineq10, gdp.thousands.per.cap)) [1] -29.96955 > print (cov(spending.per.cap, gdp.thousands.per.cap)) [1] 46.66778 > print (cov(spending.per.cap, ineq10)) [1] -10.89353 > print (cov(trust, gdp.thousands.per.cap)) [1] 112.6078 > print (cov(trust, ineq10)) [1] -38.15728 > print (cov(trust, spending.per.cap)) [1] 31.1585 > > print (cor(ineq10, gdp.thousands.per.cap)) [1] -0.3902274 > print (cor(spending.per.cap, gdp.thousands.per.cap)) [1] 0.8820613 > print (cor(spending.per.cap, ineq10)) [1] -0.5391223 > print (cor(trust, gdp.thousands.per.cap)) [1] 0.5111189 > print (cor(trust, ineq10)) [1] -0.4534901 > print (cor(trust, spending.per.cap)) [1] 0.5375404 > > print (cor(trust, spend.per.cap)) [1] 0.5375404 > > plot (gdp.thousands.per.cap, spending.per.cap) > > equation1 <- lm(trust ~ gdp.thousands.per.cap + ineq10) > summary(equation1)

Call: lm(formula = trust ~ gdp.thousands.per.cap + ineq10)

Residuals: Min 1Q Median 3Q Max -29.468 -7.454 -1.660 6.055 26.362

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 26.6664 9.2841 2.872 0.00729 ** gdp.thousands.per.cap 0.4319 0.1740 2.482 0.01867 * ineq10 -0.8597 0.4555 -1.887 0.06853 . --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 13.05 on 31 degrees of freedom Multiple R-squared: 0.3374, Adjusted R-squared: 0.2946 F-statistic: 7.892 on 2 and 31 DF, p-value: 0.001697

> > equation2 <- lm(spending.per.cap ~ gdp.thousands.per.cap + ineq10) > summary(equation2)

Call: lm(formula = spending.per.cap ~ gdp.thousands.per.cap + ineq10)

Residuals: Min 1Q Median 3Q Max -3.3448 -1.0467 -0.0041 1.4400 2.7717

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.46915 1.15278 1.274 0.21198 gdp.thousands.per.cap 0.20846 0.02160 9.650 7.44e-11 *** ineq10 -0.15840 0.05656 -2.800 0.00871 ** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.62 on 31 degrees of freedom Multiple R-squared: 0.8228, Adjusted R-squared: 0.8114 F-statistic: 72 on 2 and 31 DF, p-value: 2.235e-12