1. Suppose that from 2020 to 2025, the price level rises at a rate of 3% per year.
   1. [1] In 2025, real GDP is equal to potential, so there is no output gap. Workers and employers are bargaining the wage for the next year.

If they are backward-looking, are wages likely to increase? If so, by how much?

2. [1] Given your answer in a, will there also be an increase in the price level next year (inflation)? If so, by how much?

3. [1.5] Suppose that in 2026, an inflationary output gap opens. Workers and employers once again bargain the wage increase for the next year.

Compared to the past year (in part b), do you think that inflation will be higher or lower than in 2025?

4. [1.5] In 2027, there is still an output gap. The price of energy—an important input—increases.

Will this affect inflation? If so, will the inflation rate be higher or lower than in 2026?

y^ = 0.9 - 0.3x

x: 2 5 1 4

y: 1 2 1    -4

a. Compute the three sums of​ squares, SST,​ SSR, and​ SSE, using the defining formulas.

SST

SSR

SSE

b. Verify the regression​ identity, SST​ = SSR​ + SSE. Is this statement​ correct?

c. Determine the value of r squared

​(Round to four decimal places.)

d. Determine the percentage of variation in the observed values of the response variable that is explained by the regression.

​(Round to two decimal places.)

e. State how useful the regression equation appears to be for making predictions.

A:=<<0,-1,1>|<4,0,-2>|<2,-1,0>|<2,1,1>>;
Matrix(3, 4, [[0, 4, 2, 2], [-1, 0, -1, 1], [1, -2, 0, 1]])

(a) Use the concept of matrix Rank to argue, without performing ANY calculation, why the columns of this matrix canNOT be linerly independent.

(b) Use Gauss-Jordan elimination method (you can use ReducedRowEchelonForm command) to identify a set B of linearly independent column vectors of A that span the column space of A. Express the column vectors of A that are not included in the set B as a linear combination of the vectors in the set B.

(c) Do the columns of matrix A span the entire Euclidean space
"real^3"
? Explain why yes or why not.

2. Consider functions f : {1, 2, 3, 4, 5, 6} → {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

(a) How many of these functions are strictly increasing (i.e. f(1) < f(2) < f(3) < f(4) < f(5) < f(6))? Hint: How many different possibilities are there for the range of f? For each range of f, how many strictly increasing functions are there?

(b) How many of these functions are non-decreasing (i.e. f(1) ≤ f(2) ≤ f(3) ≤ f(4) ≤ f(5) ≤ f(6))? Hint: What are the yards? What are the trees? Or, if you prefer, what are the stars and what are the bars?

With R coding Obs: it supposed to use probability density function like X ~ Binomial( n ,p ) dbinom(X=?, n, prob) pbinom(X=?, n, prob) rbinmo(幾個符合二項分配的X, n, prob) X~Poisson (lamda) dpois(X=?, lamda) ppois (X=?, lamda) rpois (X, lamda)

Exercises 1) A food company produces canned food, and the weight of each can on the production line is in accordance with normal distribution. N (175, 102) (Unit: gram) (a) Specifications indicate that each can weight lless than 155, what is the possibility of randomly choosing a can and it being returned? (b) b) randomly pick a can, What is the probability of qualified? (c) If the company wants the possibility of the product being returned to be <2%, they should set the return policy to allow returns when the van weighs less than how much? (d) (Randomly pick a can, What is the probability of picking a can with a weight between 160 and 190?

2. X~B(n=100,p=0.1) (a) P(125 and n(1-p)>5, X will be approximated by a normal distribution, E(X)=np、Var(X)=np(1-p) calculate P(12100 and np<5, X will be approximated by a poisson distribution, E(X)=np calculate P(12

l = [0 1 -2 1 1];

d = [2 -2 4 2 2];

r = [-1 1 -1 -2 0];

b = [2 0 -6 1 4];

n = length(d);

x= zeros(n,1);

for i = 2:n

factor = l(i)/d(i-1);

d(i) = d(i) - factor*r(i-1);

b(i) = b(i) - factor*b(i-1);

end

x(n) = b(n)/d(n);

for i = n-1:-1:1

x(i) = b(i)-r(i)*x(i+1) / d(i);

end

x1 = x(1);

x2 = x(2);

x3 = x(3);

x4 = x(4);

fprintf('\nx1 = %f\nx2 = %f\nx3 = %f\nx4 = %f\n',x1,x2,x3,x4);

this is matlab code!

It's a question of getting answers using the Thomas method.

The answer should be x1=1, x2=0, x3=-1, x4=2, x5=1.

Please fix what's wrong.

Consider the randomized block design with 4 blocks and 3 treatments given above. Test H₀: there is no difference between treatment effects at α = .05.

Consider the randomized block design with 4 blocks and 3 treatments given above. What is the value of the F statistic for blocks?

Multiply this permutation: (1 3 2)(1 4 2)