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Regression and Correlation Defination:

 

Regression: 

Regression is the measure of the relationship between one dependent variable and one or more than one independent random variable.

If we have one dependent variable(i.e, Y) and only one independent variable(i.e, X) then it is called linear regression.And if we have one dependent variable and more than two independent variables then it is called multiple linear regression.


Correlation: 

Correlation gives the relationship statistic of two random variables.It measures by using correlation coefficient. Correlation Coefficient measures the strength of relationship of two variables.It's values lie between +1 to -1. If the value is +1 then both variables are strongly positively correlated, if -1 then both variables are strongly negatively correlated and if 0 then there is no relationship between two variables.

 

Regression and Correlation Sample Questions:

Question 1: Which simplest plot is used to identify the correlation between two variables?

 

(a) Box Plot

(b) Scatter Plot

(c) Bar Plot

(d) None


Answer: (b)

Explanation: With the help of a scatter diagram, we can easily identify whether the two variables are correlated or not.

 

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Question 2: Karl Pearson’s coefficient of correlation


coefficient of correlation


is also known as:

 

 

(a) Product-moment correlation coefficient

(b) Moment correlation coefficient

(c) Product correlation coefficient

(d) None


Answer: (a)

Explanation: Product-moment correlation coefficient 

 

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Question 3: Using Karl Pearson formula, calculate the correlation coefficient and identify the relationship?

 


calculate the correlation coefficient and identify the relationship

 

(a) 0.603, positively correlated

(b) -0.603, negatively correlated

(c) -0.505, negatively correlated.

(d) 0.505, positively correlated


Answer: (a)

Explanation: Positively Corelated

 

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Question 4: Which of the following is not true for the Correlation Coefficient?

 

(a) Correlation Coefficient is independent of change of origin and scale

(b) Two independent variables are uncorrelated

(c) Correlation Coefficient lies between +1 to -1

(d) Correlation Coefficient exceeds unity


Answer: (d)

Explanation: Correlation coefficient cannot exceed unity.

 

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Question 5: Which correlation technique we used for finding correlation coefficients if we are dealing with qualitative characteristics which cannot be measured quantitatively?

 

 

(a) Karl Pearson’s Correlation Coefficient

(b) Spearman’s Rank Correlation Coefficient

(c) Both a & b

d) None

Answer: (b)

Explanation: Spearman’s Rank Correlation Coefficient is the only formula we use for finding correlation coefficients.

 

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Question 6: Is Correlation coefficient the geometric mean between the regression coefficients?

 

 

(a) Yes

(b) No

(c) None

(d) Can not define


Answer: (a)

Explanation: Yes, Correlation coefficient is the geometric mean between the regression coefficients.

 

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Question 7: If angle between two lines of regression is given as


If angle between two lines of regression is

 

question


Answer: (a)

Explanation: Lines of regression become prependicular to each other.

 

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Question 8: Which of the following is not true for Regression Coefficients?

 

(a) If one of the regression coefficients is greater than unity, the other must be less than unity.

(b) Regression coefficients are independent of the change of origin but not of scale.

(c) Correlation coefficient is the geometric mean between the regression coefficients.

(d) Correlation coefficient is the arithmetic mean between the regression coefficients.


Answer: (d)

Explanation: Correlation coefficient is the geometric mean between the regression coefficients.

 

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Question 9: Find the price value of Y with corresponding value of X = 70 from the given data:

 

                                       X            Y  

Average price              65           67

Standard deviation     2.5          3.5

Correlation coefficient is 0.8.

 

(a) 75

(b) 73.8

(c) 72.6

(d) 74


Answer: (c)

Explanation: Use line of regression formula.

 

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Question 10: If ‘b’ is the slope of the lines of regression of regression of Y on X, then

 

(a) It represents the increment in the value of dependent variable Y corresponding to a unit change in the value of independent variable X.

(b) It represents the increment in the value of dependent variable X corresponding to a unit change in the value of independent variable Y.

(c) None

(d) Both


Answer: (a)

Explanation: It represents the increment in the value of dependent variable Y corresponding to a unit change in the value of independent variable X.

 

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