NUMBER OF ATTEMPTS109210OONUMBER OF TREATS5Regression LineUse the regression line to estimate the number of trials it would take to learn these tricks if adolphin received five treats per trick. Ŷ for X = 5 would beThe head dolphin trainer is pressuring you to teach the dolphins many new tricks quickly. He hasasked you to use the least-squares regression line to predict how fast the dolphins can learn tricksif you were to give them 8 treats. Which of the following is the most appropriate response?The regression line was estimated using 1 to 4 treats and should not be used to predictwhat would happen if the dolphins were given 8 treats.O Since the regression line predicts that the dolphins will need a negative number ofattempts, you can assume the dolphins need 0 attempts if given 8 treats.The regression line predicts that the dolphins will need 1.5 attempts to learn a trickthey are given 8 treats.The regression line predicts that the dolphins will need 5.5 attempts to learn a trick ifthey are given 8 treats. Suppose you are a dolphin trainer at SeaWorld. You teach the dolphins by rewarding them with fishtreats after each successful attempt at a new trick. The following table lists the dolphins, thenumber of treats per success given to each, and the average number of attempts necessary foreach to learn to perform the tricks.Dolphin Number of Treats Number of AttemptsDiana2Frederick4FatimaMarlinŶ = bX + aYou can use the preceding sample data to obtain the regression line, where Ŷ is the predicted valueof Y:b =One formula for the slope of the regression line is as follows:SP =To calculate the slope, first calculate SP and SSx:13and SSx=∞587(Hint: For SP use the computational formula and for SSx use the definitional formula.)The slope of the regression line isFrederickFatimaMarlinThe difference between Y and Ŷ for a particular sample point (observation) is called a residual.Calculate the predicted Y (Y) for each of the dolphins, and then calculate the residuals.413, and the Y intercept of the regression line isDolphin Number of Treats Number of Attempts Predicted Y (Ŷ) ResidualDiana288On the following scatter diagram of the blue sample points (circle symbol), use the orange points(square symbol) to plot the regression line. Make sure that the orange line spans the entire graph(from left to right). A line segment will automatically connect the points.

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DolphinNumber of TreatsNumber of attemptsDiana28Frederick45Fatima18Marlin37