Dashy Square VR

All icons are exported with the name in PascalCase, prefixed with BIcon. i.e icon 'alert-circle-fill' is exported as BIconAlertCircleFill, icon 'x' is exported as BIconX, and icon 'x-square-fill' is exported as BIconXSquareFill.

Dashy Square VR

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Subsets of the elements of a vector may be selected by appending to thename of the vector an index vector in square brackets. Moregenerally any expression that evaluates to a vector may have subsets ofits elements similarly selected by appending an index vector in squarebrackets immediately after the expression.

after which we could use absdet() as just another R function.As a further trivial but potentially useful example, you might like toconsider writing a function, say tr(), to calculate the trace ofa square matrix. [Hint: You will not need to use an explicit loop.Look again at the diag() function.]

gives the results of a least squares fit where y is the vector ofobservations and X is the design matrix. See the help facilityfor more details, and also for the follow-up function ls.diag()for, among other things, regression diagnostics. Note that a grand meanterm is automatically included and need not be included explicitly as acolumn of X. Further note that you almost always will preferusing lm(.) (see Linear models) to lsfit() forregression modelling.

This alternative is the older, low-level way to perform least squarescalculations. Although still useful in some contexts, it would nowgenerally be replaced by the statistical models features, as will bediscussed in Statistical models in R.

Components of lists may also be named, and in this case thecomponent may be referred to either by giving the component name as acharacter string in place of the number in double square brackets, or,more conveniently, by giving an expression of the form

Additionally, one can also use the names of the list components indouble square brackets, i.e., Lst[["name"]] is the same asLst$name. This is especially useful, when the name of thecomponent to be extracted is stored in another variable as in

As a second example, consider a function to emulate directly theMATLAB backslash command, which returns the coefficients of theorthogonal projection of the vector y onto the column space ofthe matrix, X. (This is ordinarily called the least squaresestimate of the regression coefficients.) This would ordinarily bedone with the qr() function; however this is sometimes a bittricky to use directly and it pays to have a simple function such as thefollowing to use it safely.

Note also that the analysis of variance table (or tables) are for asequence of fitted models. The sums of squares shown are the decreasein the residual sums of squares resulting from an inclusion ofthat term in the model at that place in the sequence.Hence only for orthogonal experiments will the order of inclusion beinconsequential.

would fit a five variate multiple regression with variables (presumably)from the data frame production, fit an additional model includinga sixth regressor variable, and fit a variant on the model where theresponse had a square root transform applied.

Occasionally genuinely Poisson data arises in practice and in the pastit was often analyzed as gaussian data after either a log or asquare-root transformation. As a graceful alternative to the latter, aPoisson generalized linear model may be fitted as in the followingexample:

One way to fit a nonlinear model is by minimizing the sum of the squarederrors (SSE) or residuals. This method makes sense if the observederrors could have plausibly arisen from a normal distribution.

The 2 which is subtracted in the line above represents the numberof parameters. A 95% confidence interval would be the parameterestimate +/- 1.96 SE. We can superimpose the least squaresfit on a new plot:

The standard package stats provides much more extensive facilitiesfor fitting non-linear models by least squares. The model we have justfitted is the Michaelis-Menten model, so we can use

If your device detects that the object you're measuring is a square or rectangle, it automatically places a measurement box around the object. Tap the Add button and measurements appear for the object's width and length. Move your device slightly, and the object's calculated area appears.

Power: the magnitude of the PSD is the mean-square value of the analyzed signal. It does not refer to the physical quantity of power, such as watts or horsepower. However, power is proportional to the mean-square value of some quantity, such as the square of current or voltage in an electrical circuit. The mean-square value of any quantity is the power of that quantity.

We must use the mean-square value to combine signals of different frequencies. For example, Figure 2.2 displays the summation of two sine waves with different frequencies. The mean-square value of the unit sine wave is 0.5, and the RMS value is 0.707. After the two waveforms are added together, the mean-square value is 1.0, and the RMS value is 1.0.

Mathematically, this is a general result for two independent variables A and B. The square of the sum is (A+B)2 = A2 + 2AB + B2. If the two variables are independent and have a mean value of zero, then the mean value of 2AB is also zero (Figure 2.3).

In Figure 2.5, the frequency spectrum of a car vibration signal is computed with three different frequency bandwidths. The squared magnitudes of the spectra are proportional to the frequency bandwidth. To overcome this variation, the PSD divides the squared magnitude by the frequency bandwidth to provide a consistent value independent of the bandwidth.