Tag: linear regression

Questions Related to linear regression

Rank correlation is used ________.

business economics and quantitative methods correlation analysis aspects of correlation scatter graphs and correlation linear regression

  1. only when the number of variables is smaller

  2. only when the rank is given

  3. to know the talent of the workers of two factories

  4. all of the above

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Correct Option: D
Explanation:

Rank correlation is used when the ranks are provided to the items or individuals that makes the comparison or measuring the relation between them easy  and also when the number of variables is small.

Which of the following plays a great part in interpreting the value of the relationship?

business economics and quantitative methods correlation analysis aspects of correlation scatter graphs and correlation linear regression

  1. Square of the co-efficient of correlation

  2. Probable error

  3. Scatter diagram

  4. Correlation graph

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Correct Option: B
Explanation:

The probable error of correlation coefficient helps in determining the accuracy and reliability of the value of the coefficient that so far depends on the random sampling.

The formula of product moment correlation is ______________.

business economics and quantitative methods correlation analysis aspects of correlation scatter graphs and correlation linear regression

  1. $r=\dfrac{S _{xy}}{\sqrt{S _xS _y}}$ ; S= Standard error

  2. $ r = \dfrac {{\sigma} _{xy}}{{N}{\sigma} _{x}{\sigma} _{y}}$ ; N=number of variables

  3. $ r = \dfrac {{-r}^2}{\sqrt{N}}$

  4. $ r = \dfrac {{6}{\sigma}^2 _{{d}}}{n({n}^2 - {1})}$

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Correct Option: A
Explanation:

The formula for product moment correlation given in the option A is correct and measures the linear relationship between two variables. The formula basically tries to show how strongly are the two variables (x and y in this case) are related to each other. A correlation could be weakly or strongly correlated depending on the value of 'r'. 

The formula of Karl Pearson's co-efficient of correlation is ________.

business economics and quantitative methods correlation analysis aspects of correlation scatter graphs and correlation linear regression

  1. $r = 1 - \dfrac{6\Sigma{{D} _2}}{{{N} _{3}} - N}$

  2. $r = \dfrac{{\Sigma}{x}{y}}{{N}{\sigma}{x}{\sigma}{y}}$

  3. $ r = \dfrac {{\sigma}{x}}{{\sigma}{y}}$

  4. $ r = \dfrac {{\sigma}{y}}{{\sigma}{x}}$

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Correct Option: B
Explanation:

The correct formula foe the karl pearson's coefficient if correlation is given in the option B. The value of coefficient always lies between -1 to +1 that measures the strength of linear relationship between two variables.

Defects of Karl Pearson's method is/are________.

business economics and quantitative methods correlation analysis aspects of correlation scatter graphs and correlation linear regression

  1. it consumes more time

  2. the value of correlation is affected by extreme values

  3. if the data are not homogeneous, the co-efficient of correlation will give a wrong picture

  4. all of the above

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Correct Option: D
Explanation:

Disadvantages of using karl pearson's method is that it is avery time consuming and lengthy process and it gets affected by extreme values and it may give a wrong image if the variables are not of same nature or homogeneous.

The original formula that Pearson developed is commonly known as___________.

business economics and quantitative methods correlation analysis aspects of correlation scatter graphs and correlation linear regression

  1. Probable error

  2. the product moment method

  3. concurrent deviation method

  4. short-cut method

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Correct Option: B

Karl Pearson's method is popularly known as ______________.

business economics and quantitative methods correlation analysis aspects of correlation scatter graphs and correlation linear regression

  1. concurrent deviation method

  2. correlation co-efficient

  3. technical co-efficient

  4. rank correlation

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Correct Option: B
Explanation:

Karl Pearson's method is known as correlation coefficient as it measures the degree of relationship between two variables and its value ranges between +1 to -1.

The regression is linear when the curve of the regression is_____________.

business economics and quantitative methods correlation analysis aspects of correlation scatter graphs and correlation linear regression

  1. straight line

  2. not a straight line

  3. concave to the origin

  4. convex to the origin

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Correct Option: A
Explanation:

Regression is said to be linear when the curve drawn from the data is a straight line. It measures the relationship between one dependent variable with one or more independent variables.

The problem of predicting the average value of one unknown variable from the known variable is called the problem of __________.

business economics and quantitative methods correlation analysis aspects of correlation scatter graphs and correlation linear regression

  1. correlation

  2. regression

  3. sampling distribution

  4. index number

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Correct Option: B
Explanation:

In statistical modelling, regression analysis measures the degree of relationship among variables and here, the problem of predicting the average value of unknown variable from the known variable arise.

Regression establishes______________.

business economics and quantitative methods correlation analysis aspects of correlation scatter graphs and correlation linear regression

  1. the direction and degree of relationship between two variables

  2. the direction and degree of relationship between two or more variables

  3. the degree of variability between two and more variables

  4. the functional relationship between two variables

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Correct Option: D
Explanation:

Regression measures the functional relationship between two variables in which one is a dependent variable while other variable is an independent. It measures the degree of association between the variables.