1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
umka21 [38]
3 years ago
10

A linear regression model is fitted to the data x y 37.0 65.0 36.4 67.2 35.8 70.3 34.3 71.9 33.7 73.8 32.1 75.7 31.5 77.9 with x

as the input variable and y as the output variable. Find βˆ0, βˆ1, and ˆσ2. Construct a 99% confidence interval for the expected value of the output variable when the input variable is equal to 35.
Mathematics
1 answer:
andrey2020 [161]3 years ago
6 0

Answer:

b0= 144.59

b= -2.12

Se²= 1.02

99%CI E(Y/X=35): [68.78; 71.99]

Step-by-step explanation:

Hello!

I've arranged the given data:

X: 37.0, 36.4, 35.8, 34.3, 33.7, 32.1, 31.5

Y: 65.0, 67.2, 70.3, 71.9, 73.8, 75.7, 77.9

The equation of the linear regression model is:

Yi= β₀ + βXi + εi

Where

Yi is the dependent variable

Xi is the independent variable

εi represents the errors or residues

β₀ is the intercept of the line

β is the slope

The conditions to make a linear regression analysis are:

For each given value of X, there is a population of Y~N(μy;σy²)

Each value of Y is independent of the others.

The population variances of each population of Y are equal.

From these conditions the following characteristic is deduced:

εi~N(0;σ²)

The parameters of the regression are:

β₀, β, and σ²

If the conditions are met then you can estimate the regression line:

Yi= bo * bXi + ei.

And the point estimation of the parameters can be calculated using the formulas:

β₀ ⇒ b0= (∑y/n)-b(∑x/n)

β ⇒ b= [∑xy- ((∑x)(∑y))/n]/(∑x²-((∑x)²/n))

σ²⇒ Se²= 1/(n-2)*[∑y²-(∑y)²/n - b²(∑x²-(∑x)²/n)]

n= 7

∑y= 501.80

∑y²= 36097.88

∑x= 240.80

∑x²= 8310.44

∑xy= 17204.87

b0= 144.59

b= -2.12

Se²= 1.02

The estimated regression line is:

Yi= 144.59 -2.12Xi

You need to calculate a 99%CI E(Y/X=35), the formula is:

(b0 + bX0) ± t_{n-2;1-\alpha /2}*\sqrt{S_e^2(\frac{1}{n}+\frac{(X_0-X[bar])^2}{sumX^2-(\frac{(sumX)^2}{n} )} )}

(144.59 + (-2.12*35)) ± 4.032*\sqrt{1.02(\frac{1}{7}+\frac{(35-34.4)^2}{8310.44-(\frac{(240.80)^2}{7} )} )}

[68.78; 71.99]

With a 99% confidence level youd expect that the interval [68.78; 71.99] contains the true value of the average of Y when X= 35.

I hope it helps!

You might be interested in
4 A numerical expression is shown below. Evaluate the expression.​<br><br>help please explain too
Andrews [41]

Answer:

H

Step-by-step explanation:

8 0
3 years ago
Given the function f(x) = 2x+4 and the domain: {-1,0,1},determine the range
Svetlanka [38]

Answer:

f(x) = 2x + 4 domains {-1, 0, 1}

range {2, 4, 6}

(please mark brain if this helps and is correct)

Step-by-step explanation:

to solve f(x) to find the range you would want to input all the domain numbers in the equation f(x) to get the range of all the numbers you need

step 1: take the first domain number and input it into your equation where x is

ex: 2x + 4   [2(-1) + 4] = -2 + 4 = 2

step 2: add the second domain number and input it into your equation where x is

ex: 2x + 4   [2(0) + 4] = 0 + 4 = 4

step 3: add the last domain number and input it into your equation where x is

ex: 2x + 4   [2(1) + 4] = 2 + 4 = 6

Now we have determined what the range is

6 0
3 years ago
Can anyone give me examples of this songwriting project?
scZoUnD [109]

Answer:

First find what to sing about. Next get your rythim. Last get the lyrics together.

Step-by-step explanation:

5 0
3 years ago
What is the solution ? Please help with this !!
FromTheMoon [43]

Answer:

the answer is c

Step-by-step explanation:

see picture

7 0
3 years ago
Solve.. pls need this quick.. I'll mark you as brainliest!!!
UkoKoshka [18]

Answer:

b. 896

Step-by-step explanation:

just put the numbers on the choice to know the right answer. here when you put 896 in <u>    </u>*27/14/72=24 you will get the right answer which is 24. so the answer is 896.

5 0
3 years ago
Read 2 more answers
Other questions:
  • A pool of possible jurors consists of 14 men and 10 women. How many different juries consisting of 5 men and 7 women are possibl
    14·2 answers
  • If a#b = a+2b, for integers a and b, what is the value of 3#4?
    15·1 answer
  • What is 1 and 1/2 minus 7/8
    6·2 answers
  • Let x1, x2, ...x64 be a random sample from a distribution with mean 64 and standard deviation 4. then mean and the standard devi
    6·1 answer
  • The vertex of this parabola is at (3, -2). When the x-value is 4, the y-value is 3. What is the coefficient of the squared expre
    15·2 answers
  • the 26-oz jar of chocolate fudge costs $3.12. The 16-oz jar costs $2.40. How much can you save on each ounce by choosing the bet
    6·2 answers
  • Free points insta: (jqyneii) giving Brainliest to the first person :D make sure to get outside its good for you ily &lt;3
    12·1 answer
  • PLS HELP ASAP 30 POINTS
    11·1 answer
  • PLZ HELP WILL MARK BRAINLIEST!
    14·1 answer
  • Multiply ( + 2) (2 – )
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!