Labor productivity 2020. The Division of Industrial Productivity conducted a study on United States’ labor productivity and published the result on May 28, 2020

(https://www.bls.gov/lpc/). The following shows the partial regression analysis result from the examination of the relationship between the number of employments (in thousand) and the value of production (in $ million).

SUMMARY OUTPUT Regression Statistics Multiple R 0.6889 R Square 0.4745 Adjusted R Square 0.4726 Standard Error 216513.6859 Observations 275 Variable Coefficient SE(Coeff) t-ratio P-value Intercept 3043.5544 16348.9902 0.1862 0.8525 Employment in thousand 369.8725 23.5560 15.7018 0.0000

a) We suspect that the greater the number of employments in the country, the higher is the value of production. Is the relationship statistically significant? Assuming the conditions for inference are satisfied, test an appropriate hypothesis, and state your conclusion in context.

b) Do you think that the number of employments is a useful predictor of value of production? Use the values of both R2 and s in your explanation.