3. The table shows the sleep averages and test scores of several students.

Average Sleep (h) 7 6.5 6 7.5 8 7 6.5 8 8.5 5 7 7 8 8.5 8.5 9
Test Score (%) 88 75 70 92 96 94 83 90 99 65 77 78 82 83 94 97

(a) Write the least squares regression equation that models the data. Paste an image of your spreadsheet calculations to this test.
Let x = average sleep and y = the test score.
(b) Use the equation to determine the approximate test score of a student who sleeps an average of 6 hours a night.
Show your work.

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%

Step-by-step explanation:

hey someone else has already answered this!

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%

Hope this helps!

12

step-by-step explanation:

a triangle's   full angle is 180 degrees so 180 - 156 = 24. 24/2=12