a. To find the least squares regression equation for a group of (x,y) points:
Step 1: For each point(x,y), we need to calculate x² and xy first.
Step 2: Sum all x, y, x² and xy, which gives us Σx, Σy, Σx² and Σxy
Step 3: Calculate Slope m: m = (NΣxy − Σx Σy)/ N(Σx²) − (Σx)² , here N is the number of data.
Step 4: Calculate Intercept b: b = Σy − m(Σx)/ N
Step 5: Assemble the equation as y= mx+b
Here, we have ∑x = 120, ∑y= 1379, ∑x²= 919.5, ∑xy= 10466 and N= 16
So, m= (NΣxy − Σx Σy)/ N(Σx²) − (Σx)²
= 
= 
= 
= 6.33
and b = Σy − m(Σx)/ N
= 
= 
= 
= 38.71
So, the least squares regression equation is : y= mx+b ⇒ y= 6.33x +38.71
b. When x= 8, then y= (6.33×8)+38.71 = 50.64 + 38.71 =89.35
The approximate test score of a student who sleeps an average of 8 h a night is 89.35%
Answer: H
Step-by-step explanation:
The slope can be found using two points and the formula (y2-y1)/(x2-x1)
if we use (0,-2) and (1,1), x1 = 0, y1 = -2, x2 = 1, y2 =1
plug these into the formula to get
(1- -2)/(1-0)
= 3/1
= 3
so the slope is 3, so the coefficient on the x would be 3 in the y = mx+b formula
b would equal the y-intercept or the number when x = 0
when x = 0, y = -2, so b = -2
plug these into y = mx+b to get
y = 3x -2
Answer:
2 (4x+9y)
Step-by-step explanation:
Simplified:
8x+18y
Don't know my wingspan but i'm 5'3
If you would like to solve the equation 16 = (- 5 + z) / 4, you can do this using the following steps:
16 = (- 5 + z) / 4 /*4
16 * 4 = - 5 + z
16 * 4 + 5 = z
z = 69
The correct result would be a. 69.