Tag: karl pearson's product moment method

Questions Related to karl pearson's product moment method

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

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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 $(r)=\sqrt{b _{xy}\times b _{yx}}$
                                                            $=\sqrt{\dfrac{-1}{6}\times \dfrac{-3}{2}}$

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

                                                            $=\dfrac{1}{2}$

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

    Who has coined the term Regression?

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

    1. Francis Galton

    2. R.A. Fisher

    3. Daniel

    4. Karl Pearson

    Show answer
    Correct Option: A
    Explanation:

    Regression is a technique for determining the statistical relationship between two or more variables where a change in a dependable variable is associated with and depends on a change in one or more independant variables. The term regression has been coined by Francis Galton.