How should I interpret an R-squared value that is less than zero?
As others have said, this can't happen if your linear model includes an intercept term. But if you are fitting a model without intercept, and your software is calculating [math]R^2[/math] as "variance explained," it means your model fits worse than the model which always predicts the mean of the [math]Y[/math] values.
Interpretation of derivative Word Problem?
A = P ( 1 + ( r / 100 )^n when A = 2P 2P = P ( 1 + ( r / 100 ) )^n 2 = ( 1 + ( r / 100 ) )^n ln 2 = n ln [ 1 + ( r / 100 ) ] ln 2 / ln [ 1 + ( r / 100 ) ] = n dn / dr = [ ln 2 ]* ( 1 / 100 ) /[ { 1 / [ 1 + ( r / 100 ) ] } ] dn / dr = ( 1 / 100 )ln 2 / [ 1 / [ (100 + r ) / 100 ] ] dn / dr = ( 1 / 100 ) ln 2 / [ 100 / ( 100 + r ) ] dn / dr = ( 100 + r )ln 2 / 10000 dn / dr = 105 ln 2 / 10000
How should one interpret T: R^3 -> R^2?
T is a map from a triplet of real numbers to a pair of real numbers. Consider the example below:T(x, y, z) = ( x + y, z) *where x,y,z are real numbersPlugging in values for x,y,z:T (1, 1/3, 2) = (4/3, 2)
How does one interpret large standard error with high R-square and t-value?
Basic rule #1: Never eliminate outliers unless for some valid reason you justify eliminating them (i.e miscalculation, experimental error, mixed-effect with outside parameters).Your R2 indicates a high level of explanatory power of your covariates to your response variable. Though it might be misleading especially if you have a large number of covariates. Check R2-adjusted as a first attempt and p-values of the covariates.If you feel prediction power is weak due to high SE, do some cross validation to test it. Out of sample performance is important. If so, re-assess your model.There is always a chance that the methodology you use is not fit for the problem you have. People tend to fit their problems to the solution at hand rather than finding a proper solution to the problem at hand.
How do I interpret the volatility surface of an interest rate swap?
A volatility surface has to be fit using a number of derivatives, it’s not specific to one swap.While there are some technical differences in precise definition, the general idea is that the surface tells you the implied volatility of the reference interest rate at any future time and level of interest rates.It might be easier to understand if you consider simulating an interest rate path. Suppose three-month LIBOR is 1.00% now, and at t=0, r = 1% it’s daily volatility is 0.03%. So you would simulate a draw from a distribution with that volatility and get, say, 0.98% for tomorrow. Looking at the volatility surface for t=1, r=0.98%, you’d get a new volatility, to simulate the next move. And so on into the future.
How can I find the maximum curvature of the curve r(t) =
The curve is a parabola which has a single vertex at the origin. The vertices are the local minima and maxima of curvature. With a bit of handwaving we know the minimum curvature will be at t=0. Plugging this in to the formula for curvature gives 1. If you want a more explicit way of doing this. Take the formula for curvature [math]\kappa = \frac{|x'y''-y'x''|}{(x'^2+y'^2)^{3/2}}[/math] put in the formula for your curve [math]x=t, y=t^2[/math]. Now differentiate with respect to t and find when it is zero [math]\frac{d\kappa}{dt}=0[/math]. This gives extrema, differentiate again to fin is its a maximum or minimum.
Find and interpret the annual yield corresponding to the given nominal rate!!?
I am clueless about how to solve questions like this. a) 8% compounded monthly b) 5.5% compounded quarterly If you could SHOW me how to solve it with the RIGHT answer you get ten points! Thanks!
Pearson's correlation coefficient r?
Hand calculate Pearson's correlation coefficient r for the relationship between x & y. Variable x has a mean of 3.0 & a standard deviation of 1.6; variable y has a mean of 13.0 & a standard deviation of 3.9. X Y 1 17 2 14 3 16 4 10 5 8 > Interpret Pearson's correlation coefficient r > Is the correlation statistically significant?
How would you solve this derivative word problem?
If a sum of money is deposited into an account that pays r% interest compounded annually, the doubling time (in years) is given by T=ln 2 / ln(1+r/100). Find and interpret dT/dr when r=5. Could you maybe also explain a little bit of the process for my understanding so I can interpret what is actually trying to be said here? That would be awesome, thanks! :)