At a barbershop music singing competition, choruses are judged on three scales: Music (quality of the arrangement, etc.), Performance, and Singing. The scales are supposed to be independent of each other, and each is scored by a different judge, but a friend claims that he can predict a chorus’s Singing score from the other two scores. He offers the following regression based on the scores of all 34 choruses in a recent competition:

a) What do you think of your friend’s claim? Can he predict Singing scores?
b) State the standard null hypothesis for the coefficient of Performance and complete the t-test at the 5% level. State your conclusion.
c) Complete the analysis. Check assumptions and conditions to the extent you can with the information provided.

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Dependent variable is: Singing R-squared = 90.9% R-squared (adjusted) = 90.3% s = 6.483 with 34 - 3 = 31 degrees of freedom Variable Intercept Performance Music Coefficient SE(Coeff) 2.08926 7.973 0.793407 0.0976 0.219100 0.1196 t-ratio 0.262 8.13 1.83 P-value 0.7950 ≤0.0001 0.0766