For the regression equation, Y=bX+a, which of the following X,Y points will be on the
regression line?
a, a,b
b, b,a
c, 0,a
d, 0,b
o b
To determine which points will be on the regression line, we can substitute the values of X and Y into the regression equation and check if it holds true.
Let's substitute the values of each given point into the equation Y = bX + a:
a. X = a, Y = a
Substitute into the equation: a = b(a) + a
Simplify: a = ab + a
Subtract 'a' from both sides: 0 = ab
Since 0 does not equal ab, this point (a, a) is not on the regression line.
b. X = b, Y = a
Substitute into the equation: a = b(b) + a
Simplify: a = b^2 + a
Subtract 'a' from both sides: 0 = b^2
Since 0 does not equal b^2, this point (b, a) is not on the regression line.
c. X = c, Y = 0
Substitute into the equation: 0 = bc + a
Subtract 'a' from both sides: -a = bc
Divide both sides by 'c': -a/c = b
Substitute b = -a/c into the equation: 0 = c(-a/c) + a
Simplify: 0 = -a + a
This equation holds true, which means the point (c, 0) is on the regression line.
d. X = 0, Y = b
Substitute into the equation: b = b(0) + a
Simplify: b = a
Since b equals a, this point (0, b) is on the regression line.
Therefore, the points c, 0, a and 0, b will be on the regression line.
To determine which of the given points will be on the regression line, we need to substitute the values of X and Y from each point into the regression equation and check if the equation holds true.
The regression equation is Y = bX + a.
Let's consider each option individually:
a) a, a, b:
Substituting X = a and Y = b into the equation:
Y = bX + a
a = b(a) + a
a = ab + a
This equation is not true. Therefore, the point a, a, b does not lie on the regression line.
b) b, b, a:
Substituting X = b and Y = a into the equation:
Y = bX + a
a = b(b) + a
a = b^2 + a
This equation is true. Therefore, the point b, b, a lies on the regression line.
c) c, 0, a:
Substituting X = c and Y = 0 into the equation:
Y = bX + a
0 = b(c) + a
0 = bc + a
This equation is not true. Therefore, the point c, 0, a does not lie on the regression line.
d) 0, b, c:
Substituting X = 0 and Y = b into the equation:
Y = bX + a
b = b(0) + a
b = a
This equation is true. Therefore, the point 0, b, c lies on the regression line.
In conclusion, the points that lie on the regression line are b, b, a and 0, b, c.