. You are given the following partial Stata output: . regress y x z Source SS df MS Number of obs 21 F ( 2 , 18 ) = Model 270 Prob > F Residual 90 R - squared Adj R- squared Total Root MSE yl Coef . Std . Err t P> It/ [95 % Conf . Interval ] X 1.5 Z 2.0 _cons 2.0 Fill out all the remaining entries in this Stata output. For Prob >F use Stata command Ftail . 2. Use data in file USmanufacturing2014 .dta for 51 U.S . states in 2014 where 1, k and I are measured in millions of dollars 1 = output , k = capital , 1 = labor , Inq = In (q), Ink = In (k ), Inl = In (1). (a) Give a Box-and-whisker diagram for output. Do there appear to be any outliers? (b) Give a 95% confidence interval for the population mean output. (c) Which is more variable (in levels) using coefficient of variation: output or one of the inputs? (d) Give a scatterplot along with a regression line for output against capital . Comment (e) Following regression of output against capital give a 95% confidence interval for the predicted value of output when capital equals 4000 . 3. Continue with the question 2 data . It may be helpful to look at Chapter 15.2 on the Cobb - Douglas production function in the coursepack (a ) Regress Ing on an intercept and Ink . Provide an interpretation of the coefficient of Ink in terms of elasticities (b ) Using just the regression output , manually test at level 0.05 the claim that the coefficient of Ink equals 1. (c) Regress Ing on an intercept and Inl and Ink . Are the regressors Ink and Inl jointly statistically significant at level 0.05? d) Using Stata command test , test at level 0.05 whether returns to scale are constant i.e . Test whether the coefficients of Inl and Ink sum to one . (e) The regression of Ing on an intercept , Ink, Inl, (Ink)2, ( Inl)? and ( Inl X Ink ) has R2 = 0.9536 . Do you prefer this model to the model of part (c)? Explain . (f) The regression in part (e) has residual sum of squares equal to 1.55900241 . Using this information and the Stata output from part (c) to manually perform an F-test of whether the additional regressors (Ink) 2, ( Inl) 2 and ( Inl x Ink ) are jointly statistically significant at level 0.05. (g) How do results change compared to part (c) if you use option vce ( robust )