Suppose you are a dolphin trainer at SeaWorld. You teach the dolphins by rewarding them with fish treats after each successful attempt at a new trick. The following table lists the dolphins, the...



Suppose you are a dolphin trainer at SeaWorld. You teach the dolphins by rewarding them with fish treats after each successful attempt at a new trick. The following table lists the dolphins, the number of treats per success given to each, and the average number of attempts necessary for each to learn to perform the tricks.

































Dolphin


Number of Treats


Number of Attempts

Diana26
Frederick45
Fatima18
Marlin35






You can use the preceding sample data to obtain the regression line, where Ŷ is the predicted value of Y:








Ŷ











 =








bX + a











One formula for the slope of the regression line is as follows:








b









 =








SPSSx











To calculate the slope, first calculate SP and SSx


:




SP =     , and SSx





 =     .





(Hint: For SP use the computational formula and for SSx




 use the definitional formula.)






The slope of the regression line is     , and the Y intercept of the regression line is     .







The difference between Y and Ŷ for a particular sample point (observation) is called a residual. Calculate the predicted Y (Ŷ) for each of the dolphins, and then calculate the residuals.













































Dolphin


Number of Treats


Number of Attempts


Predicted Y (Ŷ)


Residual

Diana26



Frederick45



Fatima18



Marlin35








Jun 04, 2022
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