> model1 <- lm(revpar~x1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x11+x12) > summary(model1) Call: lm(formula = revpar ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 + x12) Residuals: Min 1Q Median 3Q Max -11.2351 -0.8774 0.3239 1.2822 10.1121 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 42.38982 0.71659 59.155 < 2e-16 *** x1 -15.57117 0.49644 -31.366 < 2e-16 *** x2 0.92457 0.50024 1.848 0.06958 . x3 7.62201 0.49644 15.353 < 2e-16 *** x4 -2.29061 0.49703 -4.609 2.22e-05 *** x5 -4.00436 0.49644 -8.066 4.23e-11 *** x6 3.65274 0.49644 7.358 6.70e-10 *** x7 -1.45316 0.49644 -2.927 0.00485 ** x8 0.55581 0.49625 1.120 0.26724 x9 -0.74355 0.49644 -1.498 0.13953 x10 -0.99035 0.49617 -1.996 0.05056 . x11 0.10474 0.35093 0.298 0.76640 x12 0.21225 0.01712 12.398 < 2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 2.977 on 59 degrees of freedom Multiple R-squared: 0.9624, Adjusted R-squared: 0.9547 F-statistic: 125.8 on 12 and 59 DF, p-value: < 2.2e-16 > anova(model1) Analysis of Variance Table Response: revpar Df Sum Sq Mean Sq F value Pr(>F) x1 1 8492.3 8492.3 958.3035 < 2.2e-16 *** x2 1 0.6 0.6 0.0713 0.79043 x3 1 2209.5 2209.5 249.3305 < 2.2e-16 *** x4 1 254.4 254.4 28.7056 1.460e-06 *** x5 1 517.7 517.7 58.4180 2.199e-10 *** x6 1 426.1 426.1 48.0863 3.493e-09 *** x7 1 55.4 55.4 6.2556 0.01518 * x8 1 6.8 6.8 0.7626 0.38607 x9 1 10.2 10.2 1.1468 0.28859 x10 1 39.5 39.5 4.4552 0.03904 * x11 1 3.2 3.2 0.3612 0.55012 x12 1 1362.3 1362.3 153.7228 < 2.2e-16 *** Residuals 59 522.8 8.9 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > model2 <- lm(revpar~x1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x12) > summary(model2) Call: lm(formula = revpar ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x12) Residuals: Min 1Q Median 3Q Max -11.1341 -0.9443 0.3040 1.2190 10.2131 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 42.38527 0.71096 59.617 < 2e-16 *** x1 -15.57130 0.49266 -31.607 < 2e-16 *** x2 0.92503 0.49643 1.863 0.06731 . x3 7.62189 0.49266 15.471 < 2e-16 *** x4 -2.29039 0.49324 -4.644 1.91e-05 *** x5 -4.00448 0.49266 -8.128 2.96e-11 *** x6 3.65287 0.49266 7.415 4.90e-10 *** x7 -1.45329 0.49266 -2.950 0.00453 ** x8 0.55588 0.49246 1.129 0.26349 x9 -0.74368 0.49266 -1.510 0.13641 x10 -0.99032 0.49239 -2.011 0.04880 * x12 0.21237 0.01698 12.505 < 2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 2.954 on 60 degrees of freedom Multiple R-squared: 0.9623, Adjusted R-squared: 0.9554 F-statistic: 139.3 on 11 and 60 DF, p-value: < 2.2e-16 > anova(model2) Analysis of Variance Table Response: revpar Df Sum Sq Mean Sq F value Pr(>F) x1 1 8492.3 8492.3 973.0767 < 2.2e-16 *** x2 1 0.6 0.6 0.0724 0.78885 x3 1 2209.5 2209.5 253.1742 < 2.2e-16 *** x4 1 254.4 254.4 29.1481 1.207e-06 *** x5 1 517.7 517.7 59.3185 1.582e-10 *** x6 1 426.1 426.1 48.8276 2.626e-09 *** x7 1 55.4 55.4 6.3521 0.01440 * x8 1 6.8 6.8 0.7743 0.38239 x9 1 10.2 10.2 1.1645 0.28486 x10 1 39.5 39.5 4.5239 0.03755 * x12 1 1364.7 1364.7 156.3689 < 2.2e-16 *** Residuals 60 523.6 8.7 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > anova(model1,model2) Analysis of Variance Table Model 1: revpar ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 + x12 Model 2: revpar ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x12 Res.Df RSS Df Sum of Sq F Pr(>F) 1 59 522.85 2 60 523.64 -1 -0.78942 0.0891 0.7664 > > > model3 <- lm(revpar~x1+x2+x3+x4+x5+x6+x7+x8+x12) > summary(model3) Call: lm(formula = revpar ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x12) Residuals: Min 1Q Median 3Q Max -11.8597 -0.9701 0.2111 1.4859 11.4598 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 42.40601 0.73499 57.696 < 2e-16 *** x1 -15.57073 0.50955 -30.558 < 2e-16 *** x2 0.92291 0.51345 1.797 0.07713 . x3 7.62246 0.50955 14.959 < 2e-16 *** x4 -2.29137 0.51016 -4.491 3.14e-05 *** x5 -4.00391 0.50955 -7.858 6.99e-11 *** x6 3.65230 0.50955 7.168 1.10e-09 *** x7 -1.45272 0.50955 -2.851 0.00591 ** x8 0.55556 0.50935 1.091 0.27962 x12 0.21180 0.01755 12.065 < 2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 3.056 on 62 degrees of freedom Multiple R-squared: 0.9584, Adjusted R-squared: 0.9523 F-statistic: 158.5 on 9 and 62 DF, p-value: < 2.2e-16 > anova(model3) Analysis of Variance Table Response: revpar Df Sum Sq Mean Sq F value Pr(>F) x1 1 8492.3 8492.3 909.6132 < 2.2e-16 *** x2 1 0.6 0.6 0.0676 0.79566 x3 1 2209.5 2209.5 236.6623 < 2.2e-16 *** x4 1 254.4 254.4 27.2471 2.203e-06 *** x5 1 517.7 517.7 55.4498 3.617e-10 *** x6 1 426.1 426.1 45.6431 5.676e-09 *** x7 1 55.4 55.4 5.9378 0.01770 * x8 1 6.8 6.8 0.7238 0.39817 x12 1 1359.1 1359.1 145.5748 < 2.2e-16 *** Residuals 62 578.8 9.3 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > anova(model2,model3) Analysis of Variance Table Model 1: revpar ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x12 Model 2: revpar ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x12 Res.Df RSS Df Sum of Sq F Pr(>F) 1 60 523.64 2 62 578.84 -2 -55.206 3.1629 0.04944 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 >