7.8 A researcher has data on output per worker, Y, and capital per worker, K, both measured in thousands of dollars, for 50 firms in the textiles industry in 2001. She hypothesizes that output per worker depends on capital per worker and perhaps also the technological sophistication of the firm, TECH:

Y = β1 + β2K + β3TECH + u where u is a disturbance term. She is unable to measure TECH and decides to use expenditure per worker on research and development in 2001, R&D, as a proxy for it. She fits the following regressions (standard errors in parentheses):

Yˆ = 1.02 + 0.32K R2=0.749

(0.45) (0.04)

Yˆ = 0.34 + 0.29K + 0.05R&D R2=0.750

(0.61) (0.22) (0.15)

The correlation coefficient for K and R&D was 0.92. Discuss these regression results

(1) assuming that Y does depend on both K and TECH,

(2) assuming that Y depends only on K.