Please help with the following problem:

Linear splines allow for a smoother relationship between y and X. Consider the model yi=f(xi)+ei i=1,..,n Where x,- is a scalar and f(x,-) is a smooth function. f(x,-) could be a polynomial, for example, but due to their global nature, polynomials have the unfortunate tendency to fit part of the data well and other parts poorly. A popular alternative involves writing M f(x.-) = Z mhmm) m=1 where hm(xl-) is referred to as a basis function. A smooth function that provides flexibility without the issues arising from global polynomials is the cubic spline. A cubic spline fits local cubic polynomials to three mutually exclusive and exhaustive regions of the data. In order to achieve smoothness, it requires the first and second derivatives ofthe function to be equal at the two (known) knot points that define the regions. (a) Show that a cubic spline can be expressed as a function of six basis functions. (b) How do you interpret the coefficients in this model