As Aa 12. Computing the Suppose you are a dolphin trainer at SeaWorld. You tsach

Question

As Aa 12. Computing the Suppose you are a dolphin trainer at SeaWorld. You tsach the doiphins by rewarding them with fish treats after ead successful attampt at a new trick. The following table lists the dolphins, the number of treats per sucoess given to each, and the average number of attempts necessary for each to leam to perform the tricks Number of Number of Dolphin Treats Attempts Diana Martn3 7 Marlin You can use the preceding sample data to obtain the regression line, where Y is the predicted value of Y One formula for the slope of the regression line is as follows SP To calculate the slope, first calculate SP and SS: SP , and SSx- and ss. (Hint: For SP use the computational formula and for SS, use the definitional formula.) The slope of the regression line is and the Y intercept of the regression ine is The difference between Y and Y fora particular sample point (observation) is called a residual. Calculate the predicted Y Y) for each of the dolphins, and then calculate the residuals Number of Number of Dolphin Diana Frederick Treats Attempts Predicted Y (Y-Residual Fatima

Explanation / Answer

a. To compute the slope, b find SP and SSx.

SP=sigma (xy)-(sigma x*sigma y)/n, and SSx=sigma (x-xbar)^2

where, number of attempts is independent variable, and number of treats is dependent variable.

From information given, xbar=2.5, ybar=7

SP=65-{(10)(28)}/4=-5; SSx=sigma {(2-2.5)^2+...+(3-2.5)^2}=5

b=SP/SSx=-5/5=-1

y intercept=ybar-bxbar=7-(-1)(2.5)=9.5

The regression eqaution is: yhat=9.5-x

Substitute x with 2, 4, 1, 3 and obtain the predicted y. Subtratct yhat from y to compute the residual (observed-predicted)

yhat: 7.5, 5.5, 8.5, 6.5

Resiadual: 0.5, -0.5, -0.5, 0.5

The number of attempt sto learn for x=5 is as follows:

9.5-1*5=4.5 treats

First option is correct as computing number of attempts for 0 tricks will lead to extrapolation.

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