Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression l
ine.(The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below.
(a) x=3 hours
(b) x=4.5 hours
(c) x=13 hours
(d) x=1.5 hours
(a) x=3 hours
(b) x=4.5 hours
(c) x=13 hours
(d) x=1.5 hours
1 answer:
ŷ= 6.45x + 31.5 is the equation of the regression line for the given data
<h3>How to find the equation of the regression line for a given data?</h3>Construct the table of the data as follows:
x >>>> y >>>> x² >>>> y² >>>> xy
1 39 1 1521 39
2 45 4 2025 90
3 52 9 2704 156
4 49 16 2401 196
5 61 25 4096 305
5 72 25 5184 360
................................................................................................
20 318 80 17931 1146
.................................................................................................
∑x = 20, ∑y = 318, ∑x²= 80, ∑xy = 1146, n = 6 (number data points)
The linear regression equation is of the form:
ŷ = ax + b
where a and b are the slope and y-intercept respectively
a = ( n∑xy -(∑x)(∑y) ) / ( n∑x² - (∑x)² )
a = (6×1146 - 20×318) / ( 6×80-20² )
a = 6876-6360 / 480-400
a = 516 / 80
a = 6.45
x' = ∑x/n
x' = 20/6 = 10/3
y' = ∑y/n
y' = 318/6 = 53
b = y' - ax'
b = 53 - 6.45×(10/3)
b = 53 - 21.5
b = 31.5
ŷ = ax + b
ŷ= 6.45x + 31.5
Thus, the equation of the regression line for the given data is ŷ= 6.45x + 31.5. (The scatter plot of the data is shown in the attached image)
(a) x=3 hours
ŷ= 6.45(3) + 31.5 = 50.85
(b) x=4.5 hours
ŷ= 6.45(4.5) + 31.5 = 60.525
(c) x=13 hours
ŷ= 6.45(13) + 31.5 = 115.35
(d) x=1.5 hours
ŷ= 6.45(1.5) + 31.5 = 41.175
Learn more about regression equation on:
#SPJ1
You might be interested in
Answer:
Step-by-step explanation:
Adding 10 to both sides.
Adding to both sides.
Dividing both sides by 10.
∴
The GCF of 18 and 36 is 18. To solve this, use the picture attached. After creating the boxes, find a number that both 18 and 36 can be divided by, for example, 9. Now that you have 9, divide both 18 and 36 by 9. That equals 2 and 4. Place the numbers underneath the boxes you made previously and find another number that both 2 and 4 are divisible by. 2 and 4 are both able to be divided into 2. Do 2 divided by 2 and 4 divided by 2. Now you have the numbers 1 and 2. There aren't any numbers that can be divided into 1 and 2, so now you are left with the numbers 9 and 2. Multiply the numbers together to get a GCF of 18. Hope this helped!
