given the regression line y=42-3x what number of units are expected to increase in y if x is decreased by 2 units.
a)2
b)4
c)6
d)8
The change is caused by the term -3x
Since you are "decreasing" x by 2
we sub in x = -2
so y = 42 - 3(-2) = 42 + 6
thus the change is 6
y = -1 x +42
slope = -1 = change in y/change in x
if
change in x - -1
then
change in y /-2 = -1
so
change in y = -1 (-2)
= +2
-3(-2) = +6
thanks got it
To find the number of units that are expected to increase in y when x is decreased by 2 units, you need to substitute the new value of x into the regression equation and calculate the corresponding change in y.
Given the regression line y = 42 - 3x, we want to calculate the change in y when x is decreased by 2 units.
Step 1: Substitute the new value of x into the regression equation:
x_new = x - 2
Step 2: Substitute the value of x_new into the regression equation:
y_new = 42 - 3(x - 2)
Step 3: Simplify the equation:
y_new = 42 - 3x + 6
y_new = 48 - 3x
Step 4: Calculate the change in y:
Change in y = y_new - y
Change in y = (48 - 3x) - (42 - 3x)
Change in y = 48 - 42
Change in y = 6
Therefore, the number of units that are expected to increase in y if x is decreased by 2 units is 6 units.
Answer: c) 6