Generates a data frame for regression analysis

The output is a data frame (x1, x2, y) with user-specified correlation between x1 and x2. The y (output) variable is created according to the equation
$$ y = beta1 + beta2 * x1 + beta3 * x2 + beta4 * x1 * x2 + e. $$ The arguments determine the scales of the X matrix, the random error, and the slope coefficients.

Usage

genCorrelatedData(
  N = 100,
  means = c(50, 50),
  sds = c(10, 10),
  rho = 0,
  stde = 1,
  beta = c(0, 0.2, 0.2, 0)
)

Arguments

N

Number of cases desired

means

2-vector of means for x1 and x2

sds

2-vector of standard deviations for x1 and x2

rho

Correlation coefficient for x1 and x2

stde

standard deviation of the error term in the data generating equation

beta

beta vector of at most 4 coefficients for intercept, slopes, and interaction

Details

The vector (x1,x2) is drawn from a multivariate normal distribution in which the expected value (argument means). The covariance matrix of X is built from the standard deviations (sds) and the specified correlation between x1 and x2 (rho). It is also necessary to specify the standard deviation of the error term (stde) and the coefficients of the regression equation (beta).

Examples

## 1000 observations of uncorrelated x1 and x2 with no
## interaction between x1 and x2
dat <- genCorrelatedData(N=1000, rho=0, beta=c(1, 1.0, -1.1, 0.0))
  mcGraph1(dat$x1, dat$x2, dat$y, theta=20, phi=8,
  ticktype="detailed", nticks=10)

m1 <- lm(y ~ x1 + x2, data = dat)
plotPlane(m1, plotx1 = "x1", plotx2 = "x2")