Tag: business maths

Questions Related to business maths

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

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

  1. $|a| \le 3$

  2. $|b| > 3$

  3. $|c| < 3$

  4. $None\ of\ these$

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Correct Option: A

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 

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

  1. $ x\in R$

  2. $x\in N$

  3. $x\in I$

  4. $x\in Q$

Show answer
Correct Option: C

Standard error of regression analysis is classified as

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

  1. average of coefficient

  2. variance of residual

  3. mean of residual

  4. average of residual

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Correct Option: B
Explanation:

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

Variance of residuals also known as error variance.

The independent variable is also called: 

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

  1. Regressor

  2. Regressand

  3. Predictand

  4. None of these

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Correct Option: A
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.

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

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

  1. Correlation problem

  2. Regression problem

  3. Association problem

  4. None of these

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Correct Option: B
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.

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

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

  1. Correlation

  2. Regression

  3. Residual

  4. Slope

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Correct Option: B
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. 

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

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

  1. dependent estimation

  2. reliable estimates

  3. independent estimation

  4. unreliable estimates

Show answer
Correct Option: B
Explanation:

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

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

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

    1. weighted analysis

    2. average analysis

    3. significance analysis

    4. specification analysis

    Show answer
    Correct Option: D
    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.

    The dependent variable is also called: 

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

    1. Regression

    2. Continuous variable

    3. Regressand

    4. None of these

    Show answer
    Correct Option: C
    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.

    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 ?

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

    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. $\dfrac{35}{9},\dfrac{20}{3},0.5$

    Show answer
    Correct Option: D
    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 $(r)=\sqrt{b _{xy}\times b _{yx}}$
                                                            $=\sqrt{\dfrac{-1}{6}\times \dfrac{-3}{2}}$

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

                                                            $=\dfrac{1}{2}$

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