Question

WILL GIVE BRAINLIEST!

Answer 1

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

= $\frac{(16*10466)-(120*1379)}{(16*919.5)-(120)^{2}}$

= $\frac{167456-165480}{14712-14400}$

= $\frac{1976}{312}$

= 6.33

and b = Σy − m(Σx)/ N

= $\frac{1379-(6.33*120)}{16}$

= $\frac{1379-759.6}{16}$

= $\frac{619.4}{16}$

= 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%