I run the following regressions:
Y_1 ~ c_1 + b_1*X
Y_2 ~ c_2 + b_2*X
and I get two estimates for b_1 and b_2. What is the appropiate statistic to test if b_1 <= b_2 and is there a function for that in R?
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$\begingroup$ It seems that the appropriate procedure can be found here: stats.stackexchange.com/questions/93540/… $\endgroup$– LyxUser12345Commented Jan 2, 2019 at 14:21
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$\begingroup$ Do the "$X$" in the two regressions have any data in common? Are the regressions performed using the same technique? In brief, is there any way in which the estimates of the $b_i$ might be statistically related or not? $\endgroup$– whuber ♦Commented Jan 2, 2019 at 21:30
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$\begingroup$ The "$X$" are identical and both are linear regressions, i.e. use OLS. $\endgroup$– LyxUser12345Commented Jan 3, 2019 at 16:08
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$\begingroup$ Would it be fair to understand this situation as consisting of two replications of the same experiment, then? $X$ would represent the fixed variables and the responses would be the two vectors $Y_1,Y_2.$ $\endgroup$– whuber ♦Commented Jan 3, 2019 at 16:12
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$\begingroup$ Yes, exactly. The hypothesis could be for example: Doing sport in the morning ($X$) leads to a greater effect on productivity in the morning ($Y1$) than in the afternoon ($Y2$), i.e. ($b1 > b2$). $\endgroup$– LyxUser12345Commented Jan 3, 2019 at 16:13
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