Answer :
From the given data set: X 0 1 3 5 6 6 Y 4.9 4.6 4.1 3.7 2.5 3.4, we can plot the scatter diagram to represent the relationship between X and Y. The scatter diagram is shown below: From the scatter diagram, we can observe that the type of relation that appears to exist between X and Y is a negative linear relationship, which means that as the value of X increases, the value of Y decreases.
Given that X=2.89,
Sx=1.78, Y=2.69, Sy=1.71, r=-0.82,
we can determine the least square regression line. The formula for the least square regression line is given by
y = a + bx, where: b = r(Sy/Sx) and
a = Y - bX.
Therefore, we have: b = -0.82(1.71/1.78) = -0.795 and a = 2.69 - (-0.795)(2.89) = 5.05.
Hence, the least square regression line is y = 5.05 - 0.795x. We can graph this line on the scatter diagram as shown below: (c) Using the least square regression line equation to predict Y for X=1. We have: y = 5.05 - 0.795(1) = 4.255. Therefore, the predicted value of Y for X=1 is 4.255. Thus, the long answer with detailed explanation is as follows: :(a) From the given data set: X 0 1 3 5 6 6 Y 4.9 4.6 4.1 3.7 2.5 3.4, we can plot the scatter diagram to represent the relationship between X and Y. The scatter diagram is shown below:
From the scatter diagram, we can observe that the type of relation that appears to exist between X and Y is a negative linear relationship, which means that as the value of X increases, the value of Y decreases.(b)
Given that X=2.89, Sx=1.78, Y=2.69, Sy=1.71, r=-0.82, we can determine the least square regression line. The formula for the least square regression line is given by y = a + bx, where: b = r(Sy/Sx) and a = Y - bX.
Therefore, we have: b = -0.82(1.71/1.78) = -0.795 and a = 2.69 - (-0.795)(2.89) = 5.05. Hence, the least square regression line is y = 5.05 - 0.795x. We can graph this line on the scatter diagram as shown below: (c) Using the least square regression line equation to predict Y for X=1. We have: y = 5.05 - 0.795(1) = 4.255. Therefore, the predicted value of Y for X=1 is 4.255.
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