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  1. 9

    Statistics: given total sum of squares, find R²

    Homework Statement Given: Σ(xi - x̄)² = 500 Σ(yi - ybar)² = 800 (total sum of squares, SST)) Σ(ŷ - ybar)² = 400 (total sum of estimators, SSE) Σ(xi - x̄)²(yi) = 200 Σ(xi - x̄)²(εi) = 0 n = 1000 s² = 4 Find (or explain why you cannot find): β1 β0 variance of β R² Homework Equations [/B]...
  2. 9

    Solve simple regression problem

    Homework Statement Salaries of NBA players related to average points per game: Salary = 1 500 000 + 0.9log(points), n = 150, r^2 = 0.14 1) What is a bad players salary? 2) Interpret the coefficient in front of the aggressor 3) What would be the advantages of running it in log-log form...
  3. 9

    Simple regression: not including the intercept term

    Homework Statement The simple regression model is y = α + βx + u, where u is the error term. If you don't include α, when is β unbiased? Homework Equations y = α + βx + u The Attempt at a Solution Not including α doesn't affect whether β is unbiased because α is a constant.
  4. 9

    Find lagrangian (please check work)

    Homework Statement F(x, y) = 96xy - 4x subject to constraint of 11 = x + y Form the lagrangian. Homework Equations F(x, y) = 96xy - 4x subject to constraint of 11 = x + y The Attempt at a Solution My only question is solving 11 = x + y My book says the answer is: L...
  5. 9

    Partial derivative: please check work

    Homework Statement (50 - x - y)(x+y) - x - ((y^2)/2)) simplified: 50X - X^2 - XY - 50Y - XY - Y^2 - X - ((Y^2)/2) Homework Equations 50X - X^2 - XY - 50Y - XY - Y^2 - X - ((Y^2)/2)) The Attempt at a Solution for x: 49 - 2x - 2y for y: 50 - 2x - 3y The book has the same, except -1x and...
  6. 9

    Diagonalize matrix: please check work

    Homework Statement I am pretty sure I went completely wrong but not sure where. Please help! 2 -3 2 -5 Homework Equations 2 -3 2 -5 The Attempt at a Solution (note: I apologize for poor notation) eigenvalues = -4, 1 eigenvectors = (1/√5)(1/2), (1/√10)(3/1) The matrix is not symmetric...
  7. 9

    Eigenvector sign

    Homework Statement Find eigenvector for the root -7 of: |2 3| |3 -6| Homework Equations |2 3| |3 -6| The Attempt at a Solution I got 1 -3 But my books says -1 3 I am only wondering if this is possibly the same answer, because when I check my answer by multiplying...
  8. 9

    Total differential, level curve. (please check work)

    Homework Statement For u(x1, x2) = ax1 + bx2 a) find total differential b) Draw a representative level curve for u = ubar (u with a line over it) c) Find MRS (marginal rate of substitution) Homework Equations u(x1, x2) = ax1 + bx2 The Attempt at a Solution a) fx1 = a fx2...
  9. 9

    Partial derivative with chain rule: check work

    Homework Statement If possible, please check my work for any large errors. y = 10kl - √k - √l k = (t/5) + 5 l = 5e^t/10 Evaluate at t = 0 using chain rule. Homework Equations y = 10kl - √k - √l k = (t/5) + 5 l = 5e^t/10 The Attempt at a Solution = ∂y/∂k * dk/dt + ∂y/∂l * dl/dt = (10l -...
  10. 9

    Chain rule: y = f(t, t^2, t^3) and y = g(t, h(t), k(t^2))

    Homework Statement I am confused because for each problem there is no equation and for one no intermediate variables. Compute dy/dt when a) y = f(t, t^2, t^3) b) y = g(t, h(t), k(t^2)) Homework Equations a) y = f(t, t^2, t^3) b) y = g(t, h(t), k(t^2)) The Attempt at a...
  11. 9

    Questing about eigenvector order

    In this video https://www.youtube.com/watch?feature=player_detailpage&v=INfPkT9EkhE#t=415, the presenter gets (1, -1) and (1, -8). Why exactly is it 1, -8 and not -8, 1, for example? How do you know what order to put it in?
  12. 9

    Eigenvector order

    Homework Statement A = 2 -2 -2 5 Eigenvalues are: 6, 1 Find eigenvectors. My only question is about order. My book lists them in the opposite order as I and I am not sure where I went wrong. Homework Equations A = 2 -2 -2 5 Eigenvalues are: 6, 1 The Attempt at a...
  13. 9

    Financial mathematics: find benefits

    Homework Statement City "A" wants to measure benefits of a stadium it built. Currently admission is free and 10 000 people per month visit the stadium. In a comparable city, a similar stadium charges $5 for admission and receives 2000 visitors per month. Assume a linear demand curve...
  14. 9

    Express vector as basis

    Homework Statement Given the basis vector: e1 = 1 0 0 0 e2 = 0 1 0 0 e3 = 0 0 1 0 e4 = 0 0 0 1 Express the following vector in terms of the basis: y = 3 1 2 5 Homework Equations e1 = 1 0 0 0 e2 = 0 1 0 0 e3 = 0 0 1 0 e4 = 0 0 0 1 y = 3 1 2 5 The Attempt at a...
  15. 9

    2x + y = 8, x - z = 2. Solve by elimination and substitution

    Homework Statement 2x + y = 8, x - z = 2. Solve by elimination and substitution Homework Equations 2x + y = 8, x - z = 2 The Attempt at a Solution It cannot be solved by elimination or substitution.
  16. 9

    Finance: find present value

    Cash flow of 100 000. Interest rate = 8%, inflation = 3%. Cash flow will keep pace with any increase in prices. Find present value for first three years. Answer: Because it says "cash flow will keep pace with increase in prices", don't you not divide by the inflation rate, but instead...
  17. 9

    Finding limits

    Homework Statement I am not sure what is meant by this question: for y = x^2 - 2x, find lim x->2 ((f(x) - f(1))/(x-1)) Homework Equations for y = x^2 - 2x, find lim x->2 ((f(x) - f(1))/(x-1)) The Attempt at a Solution Normally to find the limit here I would just find the derivative...
  18. 9

    Derivatives with constants

    Homework Statement Let μ represent a positive constant. Find the derivatives of: (x^2)/(2μ) Please check work. I am confused about the "constant" part. Can't you just set μ = some positive number and find the derivative that way? Homework Equations (x^2)/(2μ) The Attempt at a Solution...
  19. 9

    Absolute value and piecewise functions

    Homework Statement Find if continuous and differentiable. I am having problems with the differentiable part. Homework Equations f(x) = x² + 3, |x| ≤ 1 f(x) = |x| + 3, |x| > 1 The Attempt at a Solution (1)^2 + 3 = 4 |1| + 3 = 4 ∴ It is continuous Now, rewriting it, you...
  20. 9

    Piecewise function: check answer

    Homework Statement Make a piecewise function. If possible, please check my work. - Salesperson has salary of $500. - On first 10 000 of sales, earns 10% commission. - On next 10 000 of sales, earns 20% commission. - Earns 25% commission on any additional sales. (note: didn't simplify to...
  21. 9

    Y = aK, a >0 Find slope

    Homework Statement y = aK, a >0... Find y' and y'' and graph. Homework Equations y = aK, a > 0 The Attempt at a Solution Having a constant "a" there and then a > 0 confuses me for graphing. y' = a y" = 0 As for graphing, y' = a, a > 0... Perhaps just a straight horizontal...
  22. 9

    Convergent limits for sequences: please help picture terms

    A limit of a sequence is definetely convergent if: If for any value of K there is an N sufficiently large that an > K for n > N, OR for any value of K there is an N sufficiently large that an<±K for n > N My only question is what exactly are K, N, an and n? What values are they? How would...
  23. 9

    Sequence of 3/4^(2k). Show is convergent, find sum

    Homework Statement Consider the sequence ak = (3)/(4^(2k)). Show is convergent, find sum. Please check work. Homework Equations ak = 3/(4^2k) let s {n} be the series associated with the sequence. Cannot write summation notation here, but k starts at 1 (k = 1 on bottom) and infinity...
  24. 9

    Convergent and Divergent Sequences

    Homework Statement Please look over my work and tell me if I did something wrong. Suppose Bn is a divergent sequence with the limit +∞, and c is a constant. Prove: lim cBn -> ∞ = +∞ for c > 0 Homework Equations N/A The Attempt at a Solution lim Bn -> ∞ = means that for some value K >...
  25. 9

    Graph {(x, y) ∈ R+² : X ≥ X’ >0, Y ≥ Y’ > 0}

    Homework Statement The consumption set of a consumer is: {(x, y) ∈ R+² : X ≥ X’ >0, Y ≥ Y’ > 0}. Graph it. I am only wondering how it looks, don't need a copy of the graph. Homework Equations {(x, y) ∈ R+² : X ≥ X’ >0, Y ≥ Y’ > 0} The Attempt at a Solution This first part, (x, y) ∈ R+²...
  26. 9

    Bounded sets: x = [1, 2] U [3, 4] c R

    Hello. Please look over my answers! Homework Statement a) Prove that this set is not convex: x = [1, 2] U [3, 4] c R b) Prove the intersection of two bounded sets is bounded Homework Equations for a) x = [1, 2] U [3, 4] c R The Attempt at a Solution a) A convex set is where...
  27. 9

    Ln(9/4) + ln (16/9) - ln (3/1)

    Homework Statement If you have, for example, 2 + 4 - 1, you can get the answer (5), by doing both: = 2 + (4 - 1) and, = (2 + 4) - 1 But the same logic does not work with logs: to get the right answer (4/3) here you must do: =(ln(9/4) + ln (16/9)) - ln (3/1) and NOT...
  28. 9

    (23)/(120x) = 1/5. Solve for X

    How is it done? Having to solve for X when X is in the denominator really confuses me. Please help!
  29. 9

    Set (1/n) equal to (n/100)

    Algebraically, how is this done? I can do it no problem if there is no fraction, but have problems when there is. (1/n) = (n/100)
  30. 9

    Very basic: constant in gravity-model of trade

    Very basic: "constant" in gravity-model of trade The gravity model of trade states that trade between countries depends on the size of their economies (bigger = more trade) and distance between them (larger = less trade). The formula is: Trade = G ((Mi*Mj)/(Distance)) Mi is size of economy...
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