A set of X and Y scores has Mx=4, SSx=10, MY=5, SSY=40, and SP=40. What is the
regression equation for predicting Y from X?
a, =0.25X-4
b, =4X+4
c, =X-6
d, =4X-11
To find the regression equation for predicting Y from X, we need to calculate the slope and the y-intercept of the equation.
The slope (b) of the regression equation can be calculated using the formula:
b = SP/SSx
Where SP is the sum of products and SSx is the sum of squares for X.
Given that SP = 40 and SSx = 10, we can calculate the slope:
b = 40/10 = 4
Therefore, the slope of the regression equation is 4.
The y-intercept (a) can be calculated using the formula:
a = MY - b * Mx
Where MY is the mean of Y scores, Mx is the mean of X scores, and b is the slope.
Given MY = 5, Mx = 4, and b = 4, we can calculate the y-intercept:
a = 5 - 4 * 4 = 5 - 16 = -11
Therefore, the y-intercept of the regression equation is -11.
Putting it all together, the regression equation for predicting Y from X is:
Y = 4X - 11
Therefore, option d is the correct regression equation: =4X-11.