Question

You are given the following partial Stata output:

regress y x z

Source | SS df MS

-------------+---------------------------------------

Model | 810                  1                               

Residual |         270               19

-------------+----------------------------------------

Total |     1080                    20

------------------------------------------------------------------------------

y |     Coef. Std. Err. t P>|t| [95% Conf. Interval]

------------------------------------------------------------------------------

  x| 9 1.5

  z| 6 3.0

Number of obs =      21
F(  2,    18) =
Prob > F      =
R-squared     =

Adj R-squared =

Root MSE =

Fill out all the remaining entries in this Stata output. For Prob>F use Stata command Ftail.

Answer 1

We will use below table to calculate remaining entries

Source	SS	DF	MS	F
Treatments	SST	k−1	SST/(k−1)	MST/MSE
Error	SSE	N−k	SSE/(N−k)
Total (corrected)	SS	N−1

Source	SS	DF	MS	F
						Treatments	SST=810	k−1 = 1	SST/(k−1) = 810/1=810	MST/MSE=810/14.21=57
Error	SSE=270	N−k=19	SSE/(N−k)=270/19=14.21
Total (corrected)	SS=1080	N−1=20

The test statistic is the F value of 9.59. Using an α of 0.05, we have F_0.05;1,19 = 4.38

Since the test statistic is much larger than the critical value, we reject the null hypothesis of equal population means and conclude that there is a (statistically) significant difference among the population means.

Hope this will be helpful. Thanks and God Bless You :)