A data set is given as follows:
Please give the best fit using the least squares with the following functions
(1) y = ax + b;
(2) y = ax + b;
and draw their respective graphs.
(Probability and Statistics)
Answers
Entering the values obtained from the data in the table based on the
given functions of y = a·x + b, and y = a·|x| + b, we have;
(1) y = -0.0614·x + 1.58772
(2) y = 0.3824·x + 0.91168
How can the best fit lines be obtained?The least squares regression formula is presented as follows;
[tex]a = \mathbf{\dfrac{\sum \left(x_i - \bar x\right) \times \left(y_i - \bar y\right) }{\sum \left(x_i - \bar x\right )^2 }}[/tex]
(1) From the data in the table, and by using MS Excel, we have;
[tex]\overline x[/tex] = -0.2
[tex]\overline y[/tex] = 1.6
[tex]\sum \left(x_i - \bar x\right) \times \left(y_i - \bar y\right)[/tex] = -1.4
[tex]\sum \left(x_i - \bar x\right )^2[/tex] = 22.8
Which gives;
[tex]a = \dfrac{-1.4}{22.8 } \approx \mathbf{-0.0614}[/tex]
1.6 ≈ b - 0.0614 × (-0.2)
b = 1.6 - 0.0614 × (0.2) = 1.58772
The equation of best fit for the function, y = a·x + b, is therefore;
y = -0.0614·x + 1.58772(2) For the function, y = a·|x| + b, we have;
[tex]\overline x[/tex] = 1.8
[tex]\overline y[/tex] = 1.6
[tex]\sum \left(x_i - \bar x\right) \times \left(y_i - \bar y\right)[/tex] = 2.6
[tex]\sum \left(x_i - \bar x\right )^2[/tex] = 6.8
Which gives;
[tex]a = \dfrac{2.6}{6.8} \approx \mathbf{0.3824}[/tex]
1.6 ≈ b + 0.3824 × (1.8)
b = 1.6 - 0.3824 × (1.8) = 0.91168
The equation of best fit for the function, y = a·|x| + b, is therefore;
y = 0.3824·x + 0.91168Learn more about the least squares regression line here:
https://brainly.com/question/15882801
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Answer:
Step-by-step explanation:
If a system of equations has infinite solutions, the graphs represented by the equations are exactly the same.
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It is known that the concentration of anesthesia in human blood decreases exponentially according to the function [tex]f(x)=k* 0.95^{x}[/tex] , where K is the initial amount of anesthesia in milligrams and X is the time in minutes since its administration, how many milligrams of anesthesia are left in the patient's blood after hour and a half if it is known that 60 mg of anesthesia is initially administered?
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Answer:
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Answers
Answer:
???
Step-by-step explanation:
1. 52 + 5 = 57
2. 57 × 12 = 684
3. Test it out
684 ÷ 12 = 57
which is wrong because of the remainder.
BUT the remainder is not possible because 12 was the number it was divided by and 12 can not go into 5
so either your question is wrong or my solution is wrong
three persons are entering a five storey building.they can go to first floor or second floor or third floor or fifth floor of the building.what is the probability that they will meet in one floor?
Answers
The probability that they will meet in one floor is 1/16.
What is the probability that they will meet in one floor?There are 3 people, and 4 possible floors.
Then the probability of going to a given floor is equal to 1 over the total number of floors:
p = 1/4.
So, let's assume that the first person goes to a given floor, for example, the second.
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Then the total probability is the product of the individual probabilities:
P = (1/4)*(1/4) = 1/16.
So the probability that they will meet in one floor is 1/16.
If you want to learn more about probabilities, you can read:
https://brainly.com/question/251701
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Answers
Answer:
x = 8
Step-by-step explanation:
There are two ways of answering this:
1.)Supplementary Angles/Linear pair:
(5x- 15) + (20x - 5) = 180°
25x - 20 = 180
25x - 20 +20 = 180 + 20
25x = 200
x = 8
2.) Vertical angles theorem:
(5x - 15) = (3x + 1)
5x - 3x -15 + 15 = 3x - 3x + 1 +15
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Answer:
the first question is 80 yards
Step-by-step explanation:
the reason why is because it is a square it has all equal sides, a square has 4 sides so it would be 4 times 20 which equals 80. Hope that helps
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
27.54
Step-by-step explanation:
73% can be considered 73/100
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Answers
Answer:
15% of the students was not chosen
Step-by-step explanation:
50-35=15%
Answer:
30%
Step-by-step explanation:
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Answers
Answer:
Most significant digit. That's the same that it's called for any number system.
Step-by-step explanation:
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Answers
Answer:
17.9
Step-by-step explanation:
In 17.899 the tenth is .8 and because nine is greater than 5 the 8 becomes a 9
So in the end it looks like 17.9
Hope that helps and have a great day!
Answer:
17.9
Step-by-step explanation:
Look at the digit after the tenth value, 8.
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Answers
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answers
Answer: C
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Step-by-step explanation:
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Answer:
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Answers
Answer:
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Answers
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Step-by-step explanation:
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Answers
[tex]\\ \rm\longmapsto 4x-2>6x+8[/tex]
[tex]\\ \rm\longmapsto 4x-6x>8+2[/tex]
[tex]\\ \rm\longmapsto -2x>10[/tex]
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Answers
Answer:
$285714.2857
Step-by-step explanation:
120000/6= 20000 (One year of interest)
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Answers
Answer:
1/4
Step-by-step explanation:
16.66 2/12 invert to decimal
8.33. 1/12 invert into decimal
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25/100 = 1/4 round them up then simplify if possible
The probability that he catches 2 red balls and 1 ball of each of the other colors is 150/792.
Given that, total number of balls=12, red number of balls =3, green number of balls=3, blue number of balls =3 and white number of balls =3.
What is the probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favorable outcomes/Total number of outcomes
Here, C(n,r)= n!/r!(n-r)!
Now, C(12, 5)= 12!/5!(12-5)!
= 12!/5!(7)!
= (12×11×10×9×8×7!)/(5×4×3×2×1)×7!
= 3×11×2×3×4
= 792
Now, C(5, 2)= 5!/2!(5-2)!
= 5!/2!(3)!
= 10
Now, C(5, 1)= 5!/1!(5-1)!
= 5
So, he catches 2 red balls and 1 ball of each of the other colors
= 10×5×3
= 150
The probability of an event = 150/792
Therefore, the probability that he catches 2 red balls and 1 ball of each of the other colors is 150/792.
To learn more about the probability visit:
https://brainly.com/question/11234923.
#SPJ2
HELP ME
Dudley Durite deposited $350 into a savings account that earns 6.5% interest compounded semi-annually. What amount was in his account at the end of 1-year?
Answers
Answer:
$373.12
Step-by-step explanation:
You want to set this up with the equation for compound interest which is [tex]A=P(1+\frac{r}{n})}^{nt}[/tex]. A stands for amount, P stands for principle which in this case is 350, r is rate which for this one is .065, ad n is the amount of times compounded per year, and since it is compounded semi annually you do 2 for 2 times a year. Your equation based on this information should look like this:
[tex]A=350(1+\frac{.065}{2})}^{(2)(1)}[/tex]
After working this out you get A = 373.12
$373.12
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Answers
Answer:
155; 2535; 65Step-by-step explanation:
Fill in the missing values as below
The first row
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Answers
Answer:
27 frames per second
Step-by-step explanation:
108 ÷ 4 = 27
Answer:
108 ÷ 4 = 27
27 frames per second
Question 4! Need help
Answers
Hope this helps :)
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Answers
Answer:
the length of base triangle is 42cm