Tag: business maths

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Questions Related to business maths

Multiple choice business maths limits and continuity of a function graphs of the form y=ax^2+bx+c some more types of functions functions and their graphs

If all the roots of $z^3 +az^2 +bz+c=0$ are of unit modulus, then

  1. $|a| \le 3$
  2. $|b| > 3$
  3. $|c| < 3$
  4. $None\ of\ these$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If roots z1, z2, z3 have unit modulus, then |z1|=|z2|=|z3|=1. By Vieta's formulas, a = -(z1+z2+z3). By triangle inequality, |a| = |z1+z2+z3| <= |z1|+|z2|+|z3| = 1+1+1 = 3.

Multiple choice business maths limits and continuity of a function graphs of the form y=ax^2+bx+c some more types of functions functions and their graphs

The solution set of the equation $(x+1)^2+[x-1]^2=(x-1)^2+[x+1]^2$ where $[x]$ and $(x)$ are the greatest integer and nearest integer to $x$, is 

  1. $ x\in R$
  2. $x\in N$
  3. $x\in I$
  4. $x\in Q$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The equation is (x+1)^2 + [x-1]^2 = (x-1)^2 + [x+1]^2. Rearranging gives (x+1)^2 - [x+1]^2 = (x-1)^2 - [x-1]^2. Let f(t) = t^2 - [t]^2. We need f(x+1) = f(x-1). Since f(t) = {t}^2 + 2{t}[t], this holds when x is an integer.

Multiple choice business maths correlation and regression analysis karl pearson coefficient of correlation karl pearson's product moment method karl's pearson method

Standard error of regression analysis is classified as

  1. average of coefficient

  2. variance of residual

  3. mean of residual

  4. average of residual
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Standard error of regression analysis is classified as variance of residuals.

Variance of residuals also known as error variance.

Multiple choice business maths correlation and regression analysis karl pearson coefficient of correlation karl pearson's product moment method karl's pearson method

The independent variable is also called: 

  1. Regressor

  2. Regressand

  3. Predictand

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A linear regression line has an equation of the form $Y=a+bX$


where $Y$ is called dependent variable or response or regressand
$X$ is called independent variable or predictors or explanatory variable or regressor
$a$ is the y-intercept and
$b$ is the slope of the line.

Multiple choice business maths correlation and regression analysis karl pearson coefficient of correlation karl pearson's product moment method karl's pearson method

To determine the height of a person when his weight is given is:

  1. Correlation problem

  2. Regression problem

  3. Association problem

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A regression analysis gives the relationship between the variables. If the weight of the person is given then to determine the height of a person we formulate it as a regression problem. 

A linear regression line has an equation of the form $Y=a+bX$

where $Y$ is called dependent variable or response or regressand
$X$ is called independent variable or predictors or explanatory variable or regressor
$a$ is the y-intercept and
$b$ is the slope of the line.

Multiple choice business maths correlation and regression analysis karl pearson coefficient of correlation karl pearson's product moment method karl's pearson method

A process by which we estimate the value of dependent variable on the basis of one or more independent variables is called: 

  1. Correlation

  2. Regression

  3. Residual

  4. Slope
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$  A process by which we estimate the value of dependent variable on the basis of one or more independent variables is called: $Regression$.

$\Rightarrow$  More specifically, regression analysis helps one understand how the typical value of the dependent variable (or 'criterion variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed.
$\Rightarrow$  Regression takes a group of random variables, thought to be predicting $Y$, and tries to find a mathematical relationship between them. 

Multiple choice business maths correlation and regression analysis karl pearson coefficient of correlation karl pearson's product moment method karl's pearson method

If all conditions or assumptions of regression analysis then simple regression can give

  1. dependent estimation

  2. reliable estimates

  3. independent estimation

  4. unreliable estimates
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The simple regression gives the reliable estimates, if all the conditions or assumptions of the regression analysis are satisfied.

Multiple choice business maths correlation and regression analysis karl pearson coefficient of correlation karl pearson's product moment method karl's pearson method

In regression analysis, testing of assumptions if these are true or not is classified as

    1. weighted analysis

    2. average analysis

    3. significance analysis

    4. specification analysis
    Reveal answer Fill a bubble to check yourself
    D Correct answer
    Explanation

    In regression analysis, testing of assumptions if these are true or not is classified as specification analysis. It refers to the determination of which independent variables to be included or excluded from a regression equation.

    Multiple choice business maths correlation and regression analysis karl pearson coefficient of correlation karl pearson's product moment method karl's pearson method

    The dependent variable is also called: 

    1. Regression

    2. Continuous variable

    3. Regressand

    4. None of these
    Reveal answer Fill a bubble to check yourself
    C Correct answer
    Explanation

    A linear regression line has an equation of the form $Y=a+bX$


    where $Y$ is called dependent variable or response or regressand
    $X$ is called independent variable or predictors or explanatory variable or regressor
    $a$ is the y-intercept and
    $b$ is the slope of the line.

    Multiple choice business maths correlation and regression analysis karl pearson coefficient of correlation karl pearson's product moment method karl's pearson method

    For the variables $x$ and $y$, the two regression lines are $6x+y=30$ and $3x+2y=25$. What are the value of $\bar{x},\bar{y}$ and $r$ respectively ?

    1. $\dfrac{20}{3},\dfrac{35}{9},-0.5$
    2. $\dfrac{20}{3},\dfrac{35}{9},0.5$
    3. $\dfrac{35}{9},\dfrac{20}{3},-0.5$
    4. $\dfrac{35}{9},\dfrac{20}{3},0.5$
    Reveal answer Fill a bubble to check yourself
    D Correct answer
    Explanation

    $6x+y=30$                    ----- ( 1 )

    $3x+2y=25$                  ----- ( 2 )
    Multiplying  equation ( 1 ) by $2$ we get,
    $\Rightarrow$  $12x+2y=60$         ---- ( 3 )
    Subtracting equation ( 2 ) from equation ( 3 ) we get,
    $\Rightarrow$  $9x=35$
    $\therefore$  $x=\dfrac{35}{9}$
    Substituting value of $x$ in equation ( 1 ) we get
    $\Rightarrow$  $6\times\dfrac{35}{9}+y=30$
    $\Rightarrow$  $\dfrac{70}{3}+y=30$
    $\Rightarrow$  $y=30-\dfrac{70}{3}$
    $\Rightarrow$  $y=\dfrac{90-70}{3}$
    $\therefore$  $y=\dfrac{20}{3}$

    $\therefore$  $\overline{x}=\dfrac{35}{9}$ and $\overline{y}=\dfrac{20}{3}$
    Now, we are going to find $r:$
    $6x+y=30$                            [ Given ]
    $6x=30-y$
    $x=\dfrac{30}{6}-\dfrac{y}{6}$
    $\Rightarrow$  $b _{xy}=\dfrac{-1}{6}$
    $3x+2y=25$              [ Given ]
    $2y=25-3x$
    $y=\dfrac{25}{2}-\dfrac{3}{2}x$
    $\Rightarrow$  $b _{yx}=\dfrac{-3}{2}$
    $\Rightarrow$  Coefficient of correlation $(r)=\sqrt{b _{xy}\times b _{yx}}$
                                                            $=\sqrt{\dfrac{-1}{6}\times \dfrac{-3}{2}}$

                                                            $=\sqrt{\dfrac{1}{4}}$

                                                            $=\dfrac{1}{2}$

                                                            $=0.5$
    $\therefore$  $r=0.5$