  We consider a non-parametric regression model $y = m(x) + \epsilon$ and
propose a novel graphical device to check whether the $r$-th ($r \geqslant 1$)
derivative of the regression function $m(x)$ is positive or otherwise. Since
the shape of the regression function can be completely characterized by its
derivatives, the graphical device can correctly identify the shape of the
regression function. The proposed device includes the check for monotonicity
and convexity of the function as special cases. We also present an example to
elucidate the practical utility of the graphical device. In addition, we employ
the graphical device to formulate a class of test statistics and derive its
asymptotic distribution. The tests are exhibited in various simulated and real
data examples.
