# Question

Consider the following sample data of X and Y:

X Y

8 ............ 22.30

6 ............ 16.71

9 ............ 25.21

6 ............ 15.84

1 ............ 2.75

8 ............ 21.22

2 ............ 5.27

1 ............ 2.32

10 ............. 27.39

7 ............ 19.35

a. Regress Y against X without any constraints. What is the regression equation? Predict Y when X = 10.

b. Force the regression line through the origin. What is the new regression equation? Predict Y when X = 10 with this equation.

c. Force the regression line to go through the point (5, 13). What is the new regression line? What is the new regression equation? Predict Y when X = 10 with this equation.

d. Regress Y against X with the constraint that the slope must be less than or equal to 2. What is the new regression equation? Predict Y when X = 10 with this equation.

X Y

8 ............ 22.30

6 ............ 16.71

9 ............ 25.21

6 ............ 15.84

1 ............ 2.75

8 ............ 21.22

2 ............ 5.27

1 ............ 2.32

10 ............. 27.39

7 ............ 19.35

a. Regress Y against X without any constraints. What is the regression equation? Predict Y when X = 10.

b. Force the regression line through the origin. What is the new regression equation? Predict Y when X = 10 with this equation.

c. Force the regression line to go through the point (5, 13). What is the new regression line? What is the new regression equation? Predict Y when X = 10 with this equation.

d. Regress Y against X with the constraint that the slope must be less than or equal to 2. What is the new regression equation? Predict Y when X = 10 with this equation.

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