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  1. 9

    Statistics: given total sum of squares, find R²

    lol yea stupid error, 0.5, sorry :(
  2. 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]...
  3. 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...
  4. 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.
  5. 9

    Find lagrangian (please check work)

    Sorry. I mean if you were NOT asked to find a maximum or minimum, and were ONLY asked to find the lagrangian and the three partial derivatives - would these two answers be correct regardless of how you solved the constraint function?
  6. 9

    Find lagrangian (please check work)

    The goal was to find an optimal value subject to the constraint... Does it matter then, and how do you know which one to pick? Also, both partial derivatives would be correct, right?
  7. 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...
  8. 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...
  9. 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...
  10. 9

    Eigenvector sign

    Thanks a lot. Just to confirm, the signs in this case do not matter and both answers are correct? I am such a noobie...
  11. 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...
  12. 9

    Total differential, level curve. (please check work)

    Yes, I should've added something about that. Thanks :-).
  13. 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...
  14. 9

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

    Sorry... If it was i.e. y = (x, y), x = (t), y = (t^2) I would get it and there my book says you do the same steps as I listed above. I'm just not sure here... y = f(t, t^2, t^3). Thus, y = dependent. t, t^2, t^3 are independent. Intermediate variables must connect the two... If that is not...
  15. 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 -...
  16. 9

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

    Does this work? dy/dt = (∂y/∂u * du/dt) + (∂y/∂v * du/dt^2) + (∂y/∂w * dw/dt^3)
  17. 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...
  18. 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?
  19. 9

    Eigenvector order

    EDIT: Never mind, I was misreading the book. Answer found.
  20. 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...
  21. 9

    Financial mathematics: find benefits

    Area of the triangle of "benefits" shown above. The area above price and below the demand curve. "Consumer surplus" and "producer surplus". But because there is no supply curve, I assume we can just find consumer surplus and call it benefits.
  22. 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...
  23. 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...
  24. 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.
  25. 9

    Finance: find present value

    Nevermind, got it: to anyone interested, what I did above was wrong, you just find the real interest rate and use the annuity formula.
  26. 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...
  27. 9

    Finding limits

    Thanks to you and everyone! There is one error on the question: it should read for f(x) = x^2 - 2x, for "for y".
  28. 9

    Finding limits

    Yes, that is the question. My only question is why not merely take the derivative and find the limit at x = 2 that way? It gives a different answer...
  29. 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...
  30. 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...
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