1. A online radio platform conducted an experiment. In the treatment condition, a playlist with customized new music suggestions was featured on the subscribers' pages (vs. no playlist in the control condition), to see if it would increase minutes per week spent listening. 3 regressions were run, predicting minutes spent listening, first based only on treatment condition (1=treatment, 0=control) and then adding average minutes listened per week in the prior month, then also adding the interaction between treatment & average minutes listened previously.

Regression 1
Coefficients:

            Estimate Std. Error t value Pr(>|t|)    

(Intercept)  115.372      1.440  80.137   <2e-16 ***

Treatment      3.769      2.036   1.851   0.0643 .  

 

Regression 2
Coefficients:

              Estimate Std. Error t value Pr(>|t|)    

(Intercept)  34.692569   0.147485  235.23   <2e-16 ***

Treatment     5.076728   0.129912   39.08   <2e-16 ***

PriorMinutes  0.801762   0.001147  699.18   <2e-16 ***

 

Regression 3
Coefficients:

                        Estimate Std. Error t value Pr(>|t|)    

(Intercept)            31.812297   0.186359 186.802   <2e-16 ***

Treatment               4.836171   0.263194  18.375   <2e-16 ***

PriorMinutes            0.800572   0.001611 496.812   <2e-16 ***

Treatment:PriorMinutes  0.034101   0.015932   3.051    0.033    

 

1. How do you interpret the coefficient of Treatment in each of the regressions?
2. How would you explain the higher estimated coefficient of Treatment in Regression 2 compared to Regression 1?
3. What would you conclude about whether the effectiveness of the treatment differed for subscribers who are frequent or infrequent listeners?  Why?
4. Using Regression 3, what would you predict for someone who previously listened for 500 minutes per week and who was in the control condition?  What would you predict for that same person if they were in the treatment condition?