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I am slightly confused about my regression results. I have a SLR model with a single, dichotomous categorical variable. The results are: 

    Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)         32709       7553   4.331 0.000184 ***
`Direct Traffic`    33291      18190   1.830 0.078290 .

I understand that the estimate for Direct Traffic + Intercept equals the mean of the respondent under the condition of Direct Traffic=1. The intercept itself represents the mean of the respondent when Direct Traffic = 0. My confusion arises from the fact that the intercept is extremely significant, while my x parameter is not. Wouldn't that mean that non-Direct Traffic explains the variability of y, while Direct Traffic doesn't? Is it because the respondent variable itself is inherently explained by a non-zero intercept?

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As you said the intercept in the mean of the respondent when Direct Traffic = 0, and null hypothesis for this t test is intercept = 0. So extremely small p value (0.0002) means we should reject the null hypothesis and accept that mean of the respondent when Direct Traffic = 0 is not zero.

The effect of "Direct Traffic" is the difference of the respondent means between "Direct traffic" and "non-Direct traffic". The null hypothesis for this t test is the effect = 0, which implies that there is no difference of the respondent means between "Direct traffic" and "non-Direct traffic". p-value = 0.08 means we have no enough evidence to reject null hypothesis, or we still need to accept that there is no difference between "Direct traffic" and "non-Direct traffic" at significant level being 0.05.

In conclusion, the results indicate that 1) the mean of the respondent is not zero, and 2) there is no difference between "Direct traffic" and "non-Direct traffic" on mean of respondent at significant level being 0.05.

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  • $\begingroup$ Thanks man, appreciate the help. In essence, the y-intercept is just a simple t-test for mean where x=0 , correct? $\endgroup$
    – Tanner
    Jul 18, 2019 at 22:38
  • $\begingroup$ Similar, but not absolutely identical. In you case, you can create a dataset only keeping the observations with x = 0. And then perform t-test, you will get the results close but not equal to the results from the model. $\endgroup$
    – user158565
    Jul 19, 2019 at 0:48
  • $\begingroup$ Why isn't it exactly the same? Aren't they both saying that the mean of the respondent isnt equal to zero? Would the t test standard deviation be different from the OLS SE? $\endgroup$
    – Tanner
    Jul 19, 2019 at 1:09
  • $\begingroup$ standard error for t-test comes from the data where x = 0. In model, the SE summarized all information from all observations without missing value on x and y. $\endgroup$
    – user158565
    Jul 19, 2019 at 1:17

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