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:
Without any studying, the score would be about 328
Step-by-step explanation:
The y-intercept of an equation represents the point where its graph crosses the y-axis. At this point the value of x is always equal to 0.
The y-intercept of the equation in this context would represent the Math SAT score of a student who did not do any studying, that is the number of hours spent studying, x = 0.
Substitute x = 0 in the given equation and solve for y;
y = 24.387(0) + 328.182
y = 328.182
Therefore, Without any studying, the score would be about 328
Answer: 22 pints of water
Step-by-step explanation:
Runelle collected river water and poured in eight jars such that each jar had 2³/₄ of water.
The total amount of water collected by Runelle from the river will therefore be the sum of all the water in the 8 jars and because they are the same, we can simply multiply the quantity in one jar by 8 to see the sum:
= Amount of water in one jar * 8 jars
= 2³/₄ * 8
= 11/4 * 8
= 22 pints of water
Answer:
about 117 times
Step-by-step explanation:
No. of possible outcomes of a cube: 6
2 out the 6 possible outcomes are less than 3,
and therefore, No. of favorable outcome: 2
P(less than 3)= No. of favorable outcome / No. of possible outcomes
=2/6 => 1/3
if you roll a standard number cube 350 times then,
Prediction= number of rolls x (P(less than 3))
=350 x 1/3
≈117 times.
Answer:
the 24-inch rod
Step-by-step explanation:
