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[1] -0.04699109 Call: lm(formula = X ~ Y) Coefficients: (Intercept) Y 652.9742 -0.1539 Call: lm(formula = X ~ Y) Residuals: Min 1Q Median 3Q Max -652.2 -639.7 -630.5 -608.0 4546.8 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 652.9742 53.0562 12.307 <2e-16 *** Y -0.1539 0.1057 -1.456 0.146 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 1622 on 958 degrees of freedom (13628 observations deleted due to missingness) Multiple R-squared: 0.002208, Adjusted R-squared: 0.001167 F-statistic: 2.12 on 1 and 958 DF, p-value: 0.1457 Paired t-test data: X and Y t = 10.087, df = 959, p-value < 2.2e-16 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 450.8772 668.6919 sample estimates: mean of the differences 559.7846

> analyzeFn(X,Y,Z) [1] 0.9773882 Call: lm(formula = X ~ Y) Coefficients: (Intercept) Y -0.4584 1.0887 Call: lm(formula = X ~ Y) Residuals: Min 1Q Median 3Q Max -16.565 -1.319 -0.600 0.075 40.634 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -0.458448 0.151558 -3.025 0.00254 ** Y 1.088747 0.006615 164.594 < 2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 3.416 on 1268 degrees of freedom (13318 observations deleted due to missingness) Multiple R-squared: 0.9553, Adjusted R-squared: 0.9553 F-statistic: 2.709e+04 on 1 and 1268 DF, p-value: < 2.2e-16 Paired t-test data: X and Y t = 10.904, df = 1269, p-value < 2.2e-16 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 0.9156577 1.3174254 sample estimates: mean of the differences 1.116542

[1] 0.9958773 Call: lm(formula = X ~ Y) Coefficients: (Intercept) Y 0.5412 1.0115 Call: lm(formula = X ~ Y) Residuals: Min 1Q Median 3Q Max -6.723 -0.304 -0.073 0.209 34.579 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.541187 0.062203 8.7 <2e-16 *** Y 1.011493 0.002533 399.3 <2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 1.406 on 1323 degrees of freedom (13263 observations deleted due to missingness) Multiple R-squared: 0.9918, Adjusted R-squared: 0.9918 F-statistic: 1.595e+05 on 1 and 1323 DF, p-value: < 2.2e-16 Paired t-test data: X and Y t = 19.592, df = 1324, p-value < 2.2e-16 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 0.6860663 0.8387476 sample estimates: mean of the differences 0.762407

[1] 0.9997812 Call: lm(formula = X ~ Y) Coefficients: (Intercept) Y 0.1983 1.0702 Call: lm(formula = X ~ Y) Residuals: Min 1Q Median 3Q Max -4.4977 -0.2360 -0.1181 0.0993 4.4916 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.1982856 0.0161458 12.28 <2e-16 *** Y 1.0702465 0.0005384 1987.90 <2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.6381 on 1730 degrees of freedom (12856 observations deleted due to missingness) Multiple R-squared: 0.9996, Adjusted R-squared: 0.9996 F-statistic: 3.952e+06 on 1 and 1730 DF, p-value: < 2.2e-16 Paired t-test data: X and Y t = 17.018, df = 1731, p-value < 2.2e-16 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 0.7598189 0.9577775 sample estimates: mean of the differences 0.8587982

[1] 0.7982435 Call: lm(formula = X ~ Y) Coefficients: (Intercept) Y 0.7178 0.8817 Call: lm(formula = X ~ Y) Residuals: Min 1Q Median 3Q Max -17.834 -2.495 -1.527 -0.772 122.298 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.71782 0.25652 2.798 0.00517 ** Y 0.88173 0.01282 68.798 < 2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 10.04 on 2695 degrees of freedom (11891 observations deleted due to missingness) Multiple R-squared: 0.6372, Adjusted R-squared: 0.6371 F-statistic: 4733 on 1 and 2695 DF, p-value: < 2.2e-16 Paired t-test data: X and Y t = -4.2664, df = 2696, p-value = 2.055e-05 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -1.2227813 -0.4527203 sample estimates: mean of the differences -0.8377508

Call: lm(formula = X ~ Y) Coefficients: (Intercept) Y -0.3390 0.9748 Call: lm(formula = X ~ Y) Residuals: Min 1Q Median 3Q Max -82.176 -0.689 0.014 0.696 13.495 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -0.33899 0.09561 -3.546 0.000407 *** Y 0.97481 0.00277 351.897 < 2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 2.844 on 1175 degrees of freedom (13411 observations deleted due to missingness) Multiple R-squared: 0.9906, Adjusted R-squared: 0.9906 F-statistic: 1.238e+05 on 1 and 1175 DF, p-value: < 2.2e-16 Paired t-test data: X and Y t = -9.0096, df = 1176, p-value < 2.2e-16 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -0.9405416 -0.6041600 sample estimates: mean of the differences -0.7723508

[1] -0.01592085 Call: lm(formula = X ~ Y) Coefficients: (Intercept) Y 9.28658 -0.04811 Call: lm(formula = X ~ Y) Residuals: Min 1Q Median 3Q Max -9.3 -9.0 -8.5 -4.8 4990.4 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 9.28658 3.29983 2.814 0.00493 ** Y -0.04811 0.05928 -0.812 0.41710 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 155 on 2598 degrees of freedom (11988 observations deleted due to missingness) Multiple R-squared: 0.0002535, Adjusted R-squared: -0.0001313 F-statistic: 0.6587 on 1 and 2598 DF, p-value: 0.4171 Paired t-test data: X and Y t = -4.1621, df = 2599, p-value = 3.257e-05 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -19.700392 -7.082235 sample estimates: mean of the differences -13.39131

Call: lm(formula = X ~ Y) Residuals: Min 1Q Median 3Q Max -3.1508 -0.3445 -0.0572 0.3029 16.2019 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.531042 0.031038 17.11 <2e-16 *** Y 1.050710 0.001729 607.73 <2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.7007 on 1697 degrees of freedom (12889 observations deleted due to missingness) Multiple R-squared: 0.9954, Adjusted R-squared: 0.9954 F-statistic: 3.693e+05 on 1 and 1697 DF, p-value: < 2.2e-16 Paired t-test data: X and Y t = 61.965, df = 1698, p-value < 2.2e-16 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 1.251819 1.333656 sample estimates: mean of the differences 1.292738

[1] 0.9952572 Call: lm(formula = X ~ Y) Coefficients: (Intercept) Y 0.8277 0.9442 Call: lm(formula = X ~ Y) Residuals: Min 1Q Median 3Q Max -18.492 -0.876 0.015 0.704 44.259 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.82769 0.03020 27.4 <2e-16 *** Y 0.94421 0.00119 793.5 <2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 2.077 on 6015 degrees of freedom (8571 observations deleted due to missingness) Multiple R-squared: 0.9905, Adjusted R-squared: 0.9905 F-statistic: 6.296e+05 on 1 and 6015 DF, p-value: < 2.2e-16 Paired t-test data: X and Y t = 5.5057, df = 6016, p-value = 3.829e-08 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 0.1109106 0.2335633 sample estimates: mean of the differences 0.172237