F-tests_1

Reg lscrap hrsemp lsales lemploy if year1987 source

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. reg lscrap hrsemp lsales lemploy if year==1987 Source | SS df MS Number of obs = 43 -------------+------------------------------ F( 3, 39) = 5.84 Model | 29.600804 3 9.86693466 Prob > F = 0.0021 Residual | 65.9147585 39 1.69012201 R-squared = 0.3099 -------------+------------------------------ Adj R-squared = 0.2568 Total | 95.5155625 42 2.27418006 Root MSE = 1.3 ------------------------------------------------------------------------------ lscrap | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- hrsemp | -.0421828 .0186758 -2.26 0.030 -.0799582 -.0044074 lsales | -.9506355 .3698358 -2.57 0.014 -1.698699 -.202572 lemploy | .9921343 .3569215 2.78 0.008 .2701923 1.714076 _cons | 11.74426 4.574703 2.57 0.014 2.491046 20.99747 ------------------------------------------------------------------------------ .test lsales lemploy In STATA: just type “ test var1 var2 var3 …” after running the regression 8

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0 c α (1 - α ) f( F ) F The F statistic (cont) reject fail to reject Is F-stat positive enough to rule out a chance correlation? Reject H 0 at sig level α if F > c
Example: Overall Significance A special case of exclusion restrictions is to test H 0 : β 1 = β 2 =…= β k = 0 Since the R 2 from a model with only an intercept will be zero, the F statistic is simply ( 29 ( 29 1 1 2 2 - - - = k n R k R F

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. reg lscrap hrsemp lsales lemploy if year==1987 Source | SS df MS Number of obs = 43 -------------+------------------------------ F( 3, 39) = 5.84 Model | 29.600804 3 9.86693466 Prob > F = 0.0021 Residual | 65.9147585 39 1.69012201 R-squared = 0.3099 -------------+------------------------------ Adj R-squared = 0.2568 Total | 95.5155625 42 2.27418006 Root MSE = 1.3 ------------------------------------------------------------------------------ lscrap | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- hrsemp | -.0421828 .0186758 -2.26 0.030 -.0799582 -.0044074 lsales | -.9506355 .3698358 -2.57 0.014 -1.698699 -.202572 lemploy | .9921343 .3569215 2.78 0.008 .2701923 1.714076 _cons | 11.74426 4.574703 2.57 0.014 2.491046 20.99747 ------------------------------------------------------------------------------ 11 Prob>F = p-value: says there’s less than a 1% chance of getting an R 2 this large just due to chance sampling variability. (In other words, these X’s are highly related to Y!)
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