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:
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Step-by-step explanation:
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Answer:
21:18
Step-by-step explanation:
The product of the perpendicular lines is a negative one. Then the value of p will be negative 3.75.
<h3>What is coordinate geometry?</h3>
Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
Given the points K(-2,5), L(1,3) and M(-5, 2p).
If KL is perpendicular to LM. Then we have
The slope of KL will be
KL = (1+2)/(3-5)
KL = -1.5
The slope of LM will be
LM = (1+6)/(3-2p)
LM = 7/(3-2p)
We know the product of the perpendicular lines is a negative one.
KL x ML = -1
-1.5 x 7/(3-2p) = -1
-10.5 = -3 + 2p
2p = -7.5
p = -3.75
More about the coordinate geometry link is given below.
brainly.com/question/1601567
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