"Lead users" describe creative individuals who are on the leading edge of an important market trend. Creativity and Innovation Management (February 2008) published an article on identifying the social network characteristics of lead users of children's computer games. Data were collected for n = 326 children, and the following variables were measured: lead-user rating (y, measured on a 5-point scale), gender (x1 = 1 if female, 0 if male), age (x2, years), degree of centrality (x3, measured as the number of direct ties to other peers in the network), and betweenness centrality (x4, measured as the number of shortest paths between peers). A first-order model for y was fit to the data, yielding the following least squares prediction equation:

ŷ = 3.58 + .01x1 - .06x2 - .01x3 + .42x4

a. Give two properties of the errors of prediction that result from using the method of least squares to obtain the parameter estimates.

b. Give a practical interpretation of the estimate of b4 in the model.

c. A test of H0: β4 = 0 resulted in a p-value of .002. Make the appropriate conclusion at α = .05.