A multiple linear regression model of the form:

\[Y=\beta_0+\beta_1X_1+ \beta_2X_2+\beta_3X_3+\beta_4X_4+\epsilon \]

is fitted to some data in Minitab which generates a table showing estimates of the parameters with associated $p$-values. Determine which variable to exclude first.

Multiple response question (2 correct out of 4) covering properties of Riemann integration. Selection of questions from a pool.

Multiple correlation question. Given the correlation coefficent of $Y$ with $X_1$ is $r_{01}$, the correlation coefficent of $Y$ with $X_2$ is $r_{02}$ and the correlation coefficent of $X_1$ with $X_2$ is $r_{12}$ then explain the proportion of variablity of $Y$. Also find the partial corr coeff between $Y$ and $X_2$ after fitting $X_1$ and find how much of the remaining variability in $Y$ is explained by $X_2$ after fitting $X_1$.

Statistics and probability. One question on multiple and partial correlation.

Multiple response question (4 correct out of 8) covering properties of convergent and divergent sequences and boundedness of sets. Selection of questions from a pool.

Determine if the following describes a probability mass function.

$P(X=x) = \frac{ax+b}{c},\;\;x \in S=\{n_1,\;n_2,\;n_3,\;n_4\}\subset \mathbb{R}$.

Multiple response question (2 correct out of 4) covering properties of continuity and differentiability. Selection of questions from a pool.

Can choose true and false for each option. Also in one test run the second choice was incorrectly entered, rest correct,  but the feedback indicates that the third was wrong.

Multiple response question (2 correct out of 4) covering properties of continuity and limits of functions. Selection of questions from a pool.

This is a simple question testing the student on their ability to calculate the lowest common multiple of two integers which are: 

Part a) - coprime;

Part b) - where the greatest common divisor between the two integers is greater than one and not equal to either given number; and

Part c) - where one of the integer is a multiple of the other. 

Find the lowest common multiple and highest common factors of given numbers. Also a question on identifying prime numbers.

Elementary operations on vectors; sum, modulus, unit vector, scalar multiple. 

multiple choice question on this week's content

Template question.  Multiple choice. 

Multiple response question (3 correct out of 6) re properties of convergent and divergent sequences. Selection of questions from a pool.

multiple choice testing sin, cos, tan of  random(0,90,120,135,150,180,210,225,240,270,300,315,330) degrees

Template question. Seven statements given and student should determine if they are true or false.  It is possible that 1,2,3,4,5 or 6 out of the 7 statements will be true and these are all equally likely.

No description given

Find the $x$ and $y$ components of the resultant force on an object, when multiple forces are applied at different angles.

Another example of finding the $x$ and $y$ components when multiple forces are applied at different angles to a particle.

Multiple choice questions. Given randomised trig functions select the possible ways of writing the domain of the function.

Multiple choice questions. Given randomised trig functions select the possible ways of writing the domain of the function.

multiple choice testing sin, cos, tan of  random(0,90,120,135,150,180,210,225,240,270,300,315,330) degrees

multiple choice testing sin, cos, tan of  random(pi/6, pi/4, pi/3) radians

multiple choice testing csc, sec, cot  of  random(pi/6, pi/4, pi/3) radians

multiple choice testing csc, sec, cot of random(30, 45, 60) degrees

multiple choice testing sin, cos, tan of  random(30, 45, 60) degrees

multiple choice testing sin, cos, tan of angles that are negative or greater than 360 degrees that result in nice exact values. 

Elementary operations on vectors; sum, modulus, unit vector, scalar multiple. 

Multiple response question (3 correct out of 6) re properties of convergent and divergent sequences. Selection of questions from a pool.

Testing whether students know how to use multiple log laws.