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Enjoy this brief demonstration of the regression module
# Create normal distributed data with mean = 0 and standard deviation = 1
## r = 0.5
data <- MASS::mvrnorm(n=100,
mu=c(0, 0),
Sigma=matrix(c(1, 0.5, 0.5, 1), 2),
empirical=TRUE)
# Add names
colnames(data) <- c("x","y")# Correlation
stats::cor(data)[2]
#> [1] 0.5
# Regression
summary(stats::lm(y ~ x, data=data.frame(data)))
#>
#> Call:
#> stats::lm(formula = y ~ x, data = data.frame(data))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -2.04822 -0.52733 0.08872 0.59843 1.86069
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 4.163e-18 8.704e-02 0.000 1
#> x 5.000e-01 8.748e-02 5.715 1.18e-07 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 0.8704 on 98 degrees of freedom
#> Multiple R-squared: 0.25, Adjusted R-squared: 0.2423
#> F-statistic: 32.67 on 1 and 98 DF, p-value: 1.18e-07mcmc <- bfw::bfw(project.data = data,
y = "y",
x = "x",
saved.steps = 50000,
jags.model = "regression",
jags.seed = 100,
silent = TRUE)
# Print the results
round(mcmc$summary.MCMC[,3:7],3)
#> Mode ESS HDIlo HDIhi n
#> beta0[1]: Intercept -0.008 50000 -0.172 0.173 100
#> beta[1]: Y vs. X 0.492 51970 0.330 0.674 100
#> sigma[1]: Y vs. X 0.863 28840 0.760 1.005 100
#> zbeta0[1]: Intercept -0.008 50000 -0.172 0.173 100
#> zbeta[1]: Y vs. X 0.492 51970 0.330 0.674 100
#> zsigma[1]: Y vs. X 0.863 28840 0.760 1.005 100
#> R^2 (block: 1) 0.246 51970 0.165 0.337 100# Create noise with mean = 10 / -10 and sd = 1
## r = -1.0
noise <- MASS::mvrnorm(n=2,
mu=c(10, -10),
Sigma=matrix(c(1, -1, -1, 1), 2),
empirical=TRUE)
# Combine data
biased.data <- rbind(data,noise)# Correlation
stats::cor(biased.data)[2]
#> [1] -0.4984437
# Regression
summary(stats::lm(y ~ x, data=data.frame(biased.data)))
#>
#> Call:
#> stats::lm(formula = y ~ x, data = data.frame(biased.data))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -5.2719 -0.8151 0.0270 0.8217 3.1083
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -0.09834 0.14868 -0.661 0.51
#> x -0.49844 0.08669 -5.750 9.75e-08 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 1.492 on 100 degrees of freedom
#> Multiple R-squared: 0.2484, Adjusted R-squared: 0.2409
#> F-statistic: 33.06 on 1 and 100 DF, p-value: 9.754e-08mcmc.robust <- bfw::bfw(project.data = biased.data,
y = "y",
x = "x",
saved.steps = 50000,
jags.model = "regression",
jags.seed = 100,
run.robust = TRUE,
silent = TRUE)
# Print the results
round(mcmc.robust$summary.MCMC[,3:7],3)
#> Mode ESS HDIlo HDIhi n
#> beta0[1]: Intercept -0.026 29844 -0.204 0.141 102
#> beta[1]: Y vs. X 0.430 29549 0.265 0.604 102
#> sigma[1]: Y vs. X 0.671 16716 0.530 0.842 102
#> zbeta0[1]: Intercept 0.138 28442 0.042 0.244 102
#> zbeta[1]: Y vs. X 0.430 29549 0.265 0.604 102
#> zsigma[1]: Y vs. X 0.392 16716 0.310 0.492 102
#> R^2 (block: 1) 0.236 29549 0.145 0.331 102These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.