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Choose the correct alternative: Both the regression coefficients cannot exceed 1

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Question

Choose the correct alternative:

Both the regression coefficients cannot exceed 1

Options

  • True

  • False

MCQ
True or False
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Solution

True

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Properties of Regression Coefficients
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Chapter 2.3: Linear Regression - Q.2

RELATED QUESTIONS

You are given the following information about advertising expenditure and sales.

  Advertisement expenditure
(₹ in lakh) (X)
Sales (₹ in lakh) (Y)
Arithmetic Mean 10 90
Standard Mean 3 12

Correlation coefficient between X and Y is 0.8

  1. Obtain the two regression equations.
  2. What is the likely sales when the advertising budget is ₹ 15 lakh?
  3. What should be the advertising budget if the company wants to attain sales target of ₹ 120 lakh?

Bring out the inconsistency in the following:

bYX = bXY = 1.50 and r = - 0.9 


For a certain bivariate data

  X Y
Mean 25 20
S.D. 4 3

And r = 0.5. Estimate y when x = 10 and estimate x when y = 16


Given the following information about the production and demand of a commodity obtain the two regression lines:

  X Y
Mean 85 90
S.D. 5 6

The coefficient of correlation between X and Y is 0.6. Also estimate the production when demand is 100.


The following data about the sales and advertisement expenditure of a firms is given below (in ₹ Crores)

  Sales Adv. Exp.
Mean 40 6
S.D. 10 1.5

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Estimate the likely sales for a proposed advertisement expenditure of ₹ 10 crores.


In a partially destroyed laboratory record of an analysis of regression data, the following data are legible:

Variance of X = 9
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8x − 10y + 66 = 0
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The two regression lines between height (X) in inches and weight (Y) in kgs of girls are,
4y − 15x + 500 = 0
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Find the line of regression of X on Y for the following data:

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The following results were obtained from records of age (X) and systolic blood pressure (Y) of a group of 10 men.

  X Y
Mean 50 140
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and `sum (x_i - bar x)(y_i - bar y) = 1120`. Find the prediction of blood pressure of a man of age 40 years.


The equations of two regression lines are 10x − 4y = 80 and 10y − 9x = − 40 Find:

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  2. bYX and bXY
  3. If var (Y) = 36, obtain var (X)
  4. r

Choose the correct alternative:

If for a bivariate data, bYX = – 1.2 and bXY = – 0.3, then r = ______


Choose the correct alternative:

If the regression equation X on Y is 3x + 2y = 26, then bxy equal to 


Choose the correct alternative:

Find the value of the covariance between X and Y, if the regression coefficient of Y on X is 3.75 and σx = 2, σy = 8


State whether the following statement is True or False: 

If bxy < 0 and byx < 0 then ‘r’ is > 0


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Arithmetic mean of positive values of regression coefficients is greater than or equal to ______


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byx is the ______ of regression line of y on x


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Obtain the two regression lines:

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Variance 25 36

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bXY . bYX = ______.


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`sum(x - overlinex)^2` = 1200, `sum(y - overliney)^2` = 300, `sum(x - overlinex)(y - overliney)` = – 250

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  2. bxy
  3. Correlation coefficient between x and y.

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