In R: write a function that inputs a vector x and a number n and
returns the first n elements of x. When n is greater than
length(x), your function should just return x.
We are not allowed to use any control flow statements
Consider the points below.
P(0, -3,0), Q(5,1,-2), R(5, 2, 1)
(a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R.
(b) Find the area of the triangle PQR. (Recall the area of a triangle is one-half the area of the parallelogram.)
QUESTION BLOCK: Linear Regression and R-squared
If we know the value of b, the slope of the regression line, we
can accurately guess the value for the correlation coefficient
without looking at the scatterplot.
True
False
For a biology project, you measure the weight in grams, and the
tail length, in millimeters (mm), of a group of mice. The equation
of the least-squares line for predicting tail length from weight
is
predicted tail length = 20 +3*weight
Suppose a mouse...
QUESTION BLOCK: Linear Regression and R-squared
If we know the value of b, the slope of the regression line, we
can accurately guess the value for the correlation coefficient
without looking at the scatterplot.
True
False
For a biology project, you measure the weight in grams, and the
tail length, in millimeters (mm), of a group of mice. The equation
of the least-squares line for predicting tail length from weight
is
predicted tail length = 20 +3*weight
Suppose a mouse...
Suppose we define a relation ~ on the set of nonzero real
numbers R* = R\{0} by for all a , b E R*, a ~ b if and only if
ab>0. Prove that ~ is an equivalence relation. Find the
equivalence class [8]. How many distinct equivalence classes are
there?
Course: Differential Geometry (Vector Calculus & Linear
Algebra)
Provide all proofs
(a) Find the formula for the distance from p to the line
y=mx
(b) prove that the set U={(x,y): y<mx} is an open
set
Consider the regression we know that f there is a strong linear
correlation between X and Z, then it is more likely that the t-test
statistics get smaller. Show and explain how. Explain what happens
if t-statistics get smaller.
. Let T : R n → R m be a linear transformation and A the
standard matrix of T. (a) Let BN = {~v1, . . . , ~vr} be a basis
for ker(T) (i.e. Null(A)). We extend BN to a basis for R n and
denote it by B = {~v1, . . . , ~vr, ~ur+1, . . . , ~un}. Show the
set BR = {T( r~u +1), . . . , T( ~un)} is a...