Exercises for Data Analytics Exercise Sheet-4 The fourth exercise is about linear regression. (4.1) Use "airquality" data set which provides air quality measurements in New York. (a) Identify variables which are strongly/weakly positively/negatively correlated. (b) Use t test and check if temperature is significantly different from 79. (c) Split the data into sample A with observations 1 to 77 and sample B with observations 78 to 153. Use t test and check if temperature is significantly different between samples A and B.

The correct statement is : W is a subspace of M2x2.

TO show that W is a subspace of M2x2, we need to verify that it satisfies the three properties of a subspace:

1. W contains the zero matrix:

The zero matrix in M2x2 is the 2x2 matrix with all entries equal  to zero, which is not in W . However , we can see that the matrix {0,0;0,0} can be obtained as the difference between two matrices in W: {9,0;0,0} -{0,ber;0,0} = {0,0;0,0}. So , W does contain the zero matrix.

2. W is closed under addition:

Let A and B be two matrices in W. Then, A ={9,0;0,0} + {0,ber;0,0} and B = {9,0;0,0} + {0,ber;0,0}, which is also in W. Therefore, W is closed under addition.

3. W is closed under scalar multiplication:

Let A be a matrix in W and c be a scalar. Then ,A = {9,0;0,0} + {0,ber;0,0}, and c A = c {9,0;0,0} + c{0,ber;0,0}.

Since {9,0;0,0} and {0,ber;0,0} are both scalar multiples of A, c {9,0;0,0} and c{0,ber;0,0} are also in W . Therefore , W is closed under scalar multiplication.

Since W satisfies all three properties of a subspace, we can conclude that W is a subspace of M2x2.

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To prove that the set S = 2Z = {2x : x ∈ Z}, the set of even integers, is equicardinal with Z, the set of all integers, we need to show that there exists a one-to-one correspondence (bijection) between the two sets.

A one-to-one correspondence between two sets exists if every element of one set is paired with a unique element from the other set, and vice versa.

Let's define a function f: Z -> S such that f(x) = 2x for every x ∈ Z.

This function assigns each integer x from Z to its corresponding even integer 2x in S.

To prove that f is a bijection, we need to show that it is both injective (one-to-one) and surjective (onto).

Injectivity: Suppose f(a) = f(b) for some a, b ∈ Z. Then, 2a = 2b. Dividing both sides by 2, we get a = b. Hence, f is injective.

Surjectivity: For every y ∈ S, y = 2x for some x ∈ Z. Choosing x = y/2, we have f(x) = 2x = y. Therefore, f is surjective.

Since f is both injective and surjective, it is a bijection. Thus, S and Z are equicardinal sets.

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Answer:

x= 24 and y = 6

Step-by-step explanation:

I think that the right answer

Answer:

Step-by-step explanation:

To find each probability you will state the probability of the first event happening and multiply it by the chance of the second event happening.  

P(2 Nickels):  6/10 x 5/9 = 30/90 (1/3 chance)

P(2 Dimes):  4/10 x 3/9 = 12/90 (4/30 chance)

P(1 nickel and 1 dime): 6/10 x 4/9 = 24/90 (8/30 chance)

I hope this helps :D

Answer: It’s 3

Step-by-step explanation:

Hoped I help :)

Since events A and B are mutually exclusive, they cannot occur together. Therefore, the probability of the union of events A and B is equal to the sum of their individual probabilities. P(AUB) = P(A) + P(B) - P(A ∩ B) Where, P(A) = 0.9P(B) = 0.1Since the events are mutually exclusive, P(A ∩ B) = 0Thus,P(AUB) = P(A) + P(B) - P(A ∩ B)= 0.9 + 0.1 - 0= 1 Hence, the value of P(AUB) is 1.

The most common method for distinguishing between integers and non-integers is the decimal numeral system. It is the expansion to non-number quantities of the Hindu-Arabic numeral framework. Decimal notation is the method used to represent numbers in the decimal system.

Decimal spots are places of the digits to one side of a decimal point. The process of reducing a decimal number to a specified degree of accuracy is known as rounding. To do this we find the decimal spot we wish to adjust to and check out at the digit to one side of that number.

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In order to test if we have adopted the wrong functional forms of independent variables in a regression model Y = α + βX + u, we can use diagnostic plots of the residuals.

Residuals are the differences between the actual values of the dependent variable and the predicted values of the dependent variable. We can plot the residuals against the independent variables to check if there is any functional form that has not been captured by the model, which would indicate that the model has adopted the wrong functional form of independent variables.

If there is no pattern in the residuals when plotted against the independent variables, then it can be concluded that the model has captured the correct functional form of the independent variables. However, if there is a pattern in the residuals, it would indicate that there is some functional form that has not been captured by the model, and we would need to explore different functional forms of the independent variables to see which one fits the data better. This can be done by using different functional forms of the independent variables, such as polynomial, logarithmic, exponential, etc., and comparing the results using various statistical tests.

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If the residuals are normally distributed, then it suggests that the functional form of the independent variable is correct. If they are not, then it suggests that the functional form of the independent variable is incorrect.Overall, it is important to test for the functional forms of independent variables to ensure that the results of the regression model are unbiased and accurate.

In a regression model, it is important to make sure that the functional forms of the independent variables are correct. If they are not, the results of the model may be biased and incorrect. There are several ways to test if the functional forms are correct or not. Below are some of the methods:Plotting the residuals against the independent variable: If the functional form of the independent variable is correct, then the residuals should be randomly distributed around zero, without showing any patterns. If there are patterns in the residuals, then it suggests that the functional form is incorrect. Testing for linearity: One way to test for linearity is by including the square or cubic terms of the independent variable in the model and testing their significance. If the squared or cubic term is significant, then it suggests that the functional form of the independent variable is incorrect. Testing for additivity: One way to test for additivity is by including interaction terms between the independent variables and testing their significance. If the interaction term is significant, then it suggests that the functional form of the independent variable is incorrect. Testing for normality: One way to test for normality is by examining the normal probability plot of the residuals.

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Answer:

20 books

Step-by-step explanation:

Well 14 books in 7 months.

Find the unit rate

14/7=2

So 2 books each month

We have Ruth here that was in the book club for 10 months.

And since 2 books each month,

2*10=20

20 books

Answer: x= −27 or x = 27

Step-by-step explanation:

Answer:

-27

Step-by-step explanation:

Subtract 2 from both sides

2x= -54

Divide both sides by 2

x = -27

Answer:

234.9 million km

Step-by-step explanation:

The central angle is a quarter of a circle: 360° / 4 = 90°. Use the central angle calculator to find arc length. You can try the final calculation yourself by rearranging the formula as: L = θ * r. Then convert the central angle into radians: 90° = 1.57 rad, and solve the equation: L = 1.57 * 149.6 million km. L = 234.9 million km.

(a) If you measure a wound to be 2.5 inches long, the corresponding length in millimeters is 63.5 mm.

(b) If you measure the depth of a wound to be 0.25 inches, the corresponding length in millimeters is 6.35 mm.

If you measure a wound to be 2.5 inches long, the corresponding length in millimeters is calculated as follows;

1 in = 25.4 mm

2.5 in = ?

? = 2.5 x 25.4 mm

? = 63.5 mm

If you measure the depth of a wound to be 0.25 inches, the corresponding length in millimeters is calculated as follows;

1 in = 25.4 mm

0.25 in = ?

? = 0.25 x 25.4 mm

? = 6.35 mm

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Answer:

x = 4

Step-by-step explanation:

Given

[tex]\frac{x-2}{4}[/tex] = [tex]\frac{3x-7}{10}[/tex] ( cross- multiply )

4(3x - 7) = 10(x - 2) ← distribute parenthesis on both sides )

12x - 28 = 10x - 20 ( subtract 10x from both sides )

2x - 28 = - 20 ( add 28 to both sides )

2x = 8 ( divide both sides by 2 )

x = 4

Answer:

1.8 inches

Step-by-step explanation:

1. find the # of inches that represents 1 foot.

3/25 = 0.12in

2. to find the length of the line segment that represents 15 feet, multiply 0.12 inches by 15.

0.12*15 = 1.8in

The surface area of the cylinder is 60π cm².

What is the surface area of a cylinder?

The surface area of a cylinder indicates the total area of two plane surfaces (bases) and one curved surface.

If a cylinder has a radius of r cm and height of h cm, then the total surface area of the cylinder = 2πr(r + h)

Given, r = 3 cm and h = 7 cm.

Therefore, the total surface area of the cylinder

= 2πr(r + h)

= 2π × 3(3 + 7) cm²

= 2π × 3 × 10 cm²

= 60π cm²

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Answer:

C. 60π cm2

Step-by-step explanation:

Answer:

H

Step-by-step explanation:

The rectangle has a length of (2x + 1) and a width of (5x - 4).

And we want to select the expression that represents the rectangle's area.

Recall that a rectangle's area is simply its length multiplied by its width. Thus:

[tex]A=(2x+1)(5x-4)[/tex]

Expand by distributing:

[tex]A=(2x+1)(5x)+(2x+1)(-4)[/tex]

Distribute:

[tex]A=(10x^2+5x)+(-8x-4)[/tex]

Simplify:

[tex]A=10x^2-3x-4[/tex]

Hence, our answer is H.

Answer:

I don't know.

Step-by-step explanation:

Answer:

option a is the answer to the question

Answer:

Brand A

Step-by-step explanation:

The volume (V) of a cone is calculated as

V = [tex]\frac{1}{3}[/tex]πr²h ( r is the radius and h the height )

Brand A

V = [tex]\frac{1}{3}[/tex]π × 6² × 15 = [tex]\frac{1}{3}[/tex]π × 36 × 15 = π × 12 × 15 = 180π in³

Brand B

V = [tex]\frac{1}{3}[/tex]π × 5² × 18 = π × 25 × 6 = 150π in³

Brand A have the largest volume

Answer:

Steps:

SA = 2LW + 2WH + 2LH

SA = 2(9×2) + 2(2×11/2) + 2(9×11/2)

SA = 2×18 + 2×22/2 + 2×99/2

SA = 36 + 22 + 99

SA = 157 in²

Answer:

2m+12

Step-by-step explanation:

add like terms

2m+12

9514 1404 393

Answer:

  9

Step-by-step explanation:

There are 9 such numbers:

  1040, 2080, 3120, 4160, 5200, 6240, 7280, 8320, 9360

_____

For each ABCD, where BCD = x, we want ...

  26x = 1000A +x

  25x = 1000A

  x = 40A

The digit A ranges from 1 to 9 for a 4-digit number. That means there are 9 such numbers. For A=1, for example, x = 40·1 = 40, so the number ABCD is 1040. 26·BCD = 26·040 = 1040 as required.

Answer:

9 is correct but if you are here from caribou math it is 7

Step-by-step explanation:

don't dislike what they said because it is the right formula. 25x = 1000A

you get 1040 2080 3120 4160 5200 6240 7280 8320 9360. But since caribou asks for bcd, b > 0 because its a 3 digit number. from that we can eliminate 1040 and 2080 getting 7

Answer: C!!!!!!!

Step-by-step explanation:

Decomposers ( however you spell it ) are things that eat and uhh remove the waste and let other decompopers eat they waste

Answer:

this is hard to tell and sorry if I'm wrong but I would say it is only a

Step-by-step explanation:

Aanything in the shaded area is correct if it's not it's wrong

The random walk with absorbing barriers on the set {0, 1, 2, 3, 4} can be represented as a Markov chain with a transition probability matrix. This chain is irreducible since it is possible to reach any state from any other state. By evaluating the probabilities and the corresponding states, we can find the expected value E(X5 | X3 = 1, X0 = 2) for the given random walk with absorbing barriers.

(a) The graphical diagram representing the random walk with absorbing barriers on {0, 1, 2, 3, 4} can be visualized as a directed graph. Each state is represented by a node, and the arrows indicate the transition probabilities between states according to the given transition probability matrix P.

(b) The chain is irreducible because it is possible to reach any state from any other state. Starting from any state, there is always a positive probability of transitioning to any other state, including the absorbing states (0 and 4). This means that the chain does not have any disjoint subsets of states that are unreachable from one another.

(c) To find E(X5 | X3 = 1, X0 = 2), we condition on the starting state X0 = 2 and the state at time step 3, X3 = 1. Given this condition, we can calculate the expected value of X5, which represents the expected state at time step 5.

To compute this expectation, we can use the Markov property, which states that the future behavior of the chain depends only on its current state. Since X3 = 1 is known, we only need to consider the possible transitions from state 1 to other states according to the transition probability matrix P. By following these transitions, we can calculate the probability of reaching each state at time step 5 and then compute the expected value of X5 accordingly.

By evaluating the probabilities and the corresponding states, we can find the expected value E(X5 | X3 = 1, X0 = 2) for the given random walk with absorbing barriers.

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Answer:

its 2

Step-by-step explanation:

I have consulted many nice people ( my idiot friends) they all say 2 good luck

Answer: 4x-3

Step-by-step explanation: use the slope formula to calculate the slope, then add the y-int to the equation and ur done hope this helps

Answer:

Step-by-step explanation:

Two boys want to balance a seesaw perfectly. One boy weighs 240 pounds and is sitting four feet from the fulcrum. The other boy weighs 160 pounds. Where should the lighter boy sit to balance the seesaw?

We solve using the formula

Distance on the fulcrum × Weight of the boy

= 4 × 240 = x × 160

4 × 240 = 160x

x = 4 × 240/169

Answer:

The distance between corner to corner is equal to √10 times the width.

D = √10*W

Step-by-step explanation:

For a rectangle of length L and width W, the distance between two opposite corners can be calculated if we use the Pythagorean's theorem, where we can think on the length as one cathetus, the width as another cathetus and the diagonal as the hypotenuse.

Then the length of the diagonal is:

D^2 = L^2 + W^2

D = √( L^2 + W^2)

In this case we know that the length is 3 times the width, then:

L = 3*W

Replacing this in the equation for the diagonal we have:

D = √( (3*W)^2 + W^2) = √( 9*W^2 + W^2)

D = √( 10*W^2) = √10*√W^2 = √10*W

D = √10*W

The distance between corner to corner is equal to √10 times the width.

Answer:

the eanswer should be 12

Step-by-step explanation:

i took the test