## Related questions with answers

During new product development, companies often involve “lead users,” i.e., creative individuals who are on the leading edge of an important market trend. Creativity and Innovation Management (Feb. 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 measured: lead-user rating ( y , measured on a 5-point scale), gender (

$x _ { 1 } = 1$

if female, 0 if male), age

$\left( x _ { 2 } , \text { years } \right)$

degree of centrality (

$x _ { 3 }$

, measured as the number of direct ties to other peers in the network), and betweenness centrality (

$x_4$

, 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:

$\hat { y } = 3.58 + .01 x _ { 1 } - .06 x _ { 2 } - .01 x _ { 3 } + .42 x _ { 4 }$

Give a practical interpretation of the estimate of

$\beta _ { 4 }$

in the model.

Solution

VerifiedGiven:

$\begin{aligned} \hat{y}&=3.58+0.01x_1-0.06x_2-0.01x_3+0.42x_4 \\ n&=\text{Sample size}=326 \\ k&=\text{Number of independent variables}=4 \end{aligned}$

The coefficient of $x_4$ is 0.42.

$\hat{\beta}_4=0.42$

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