REGRESSION
Type -1
1) X: 1 2 3 4 5
Y: 3 2 5 4 6 Fit a least square line to the data in the following table using, Find regression equation y on x. y= 0.8 x + 1.6
2) X: 4 5 6 8 11
Y: 12 10 8 7 5 Obtain two lines of regression from the following data:. y= - 0.93x + 14.72; x= - 0.98y + 15.03
3) Find two regression from the following data:
X: 38 48 43 40 41
Y: 31 38 43 33 35 y= 0.79x+ 2.69, x= 0.52y + 23.18
4) Using the following data, determine the estimated value of x when y= 22 with the help of suitable regression line
X: 4 5 8 9 11 12 14
Y: 16 10 8 7 6 5 4 98x = 1530 - 81y, - 18/7
Type-2
1) Find the value of correlation coefficient, when
A) bᵧₓ= -0.4 and bₓᵧ= -0.9. 0.6
B) bᵧₓ= 1.4 and bₓᵧ= 0.3. 0.65
C) bᵧₓ= 0.9 and bₓᵧ= 0.2.
D) Regression coefficient of y on x and x on y are 1.2 and 0.3 respectively. 0.6
E) σₓ= 10, σᵧ = 12 and bᵧₓ= - 0.8. 0.67
F) σₓ= 5, σᵧ = 4 and bₓᵧ= 0.75. 0.6
2)A) If r= 0.4, Cov(x,y)= 10 and σᵧ = 5, find σₓ. 5
B) If r= 0.6, Cov(x,y)= 12 and σₓ= 5, find σᵧ 4
C) If r= 0.4, σₓ= 5, σᵧ = 5, find Cov(x,y) 10
D) σₓ= 36, bₓᵧ= 0.8, r = 0.5, find σᵧ. 22.5
E) σᵧ= 4, bᵧₓ= 0.48, r = 0.6, find σₓ. 5
3) Find the regression equation of y on x from the following values:
A) mean of x and y are 20 and 25 respectively and bᵧₓ= 0.48. y= 0.48x + 15.4
B) mean of x and y are 10 and 15 respectively and bᵧₓ= 2.5. 2y= 5x - 20
4) Find the regression equation of x on y from the following values:
A) mean of x and y are 90 and 70 respectively and bₓᵧ= 0.48. x= 1.36y + 5.2
B) mean of x and y are 15 and 10 respectively bₓᵧ=2.5. x= 2.5y - 10
5) Find the regression equation from the following values:
A) mean of x and y are 3 and 4 respectively and bₓᵧ= bᵧₓ= 0.9. y= 0.9x+ 1.3, x= 0.9y - 0.6
B) mean of x and y are 4 and 5 respectively and bₓᵧ= 0.65, bᵧₓ= 0.35. y= 0.35x+ 3.6 , x= 0.65y + 0.75
C) mean of x and y are 4 and 5 respectively and bₓᵧ=0.69, bᵧₓ= 0.39. y= 0.39x+ 3.44, x= 0.69y + 0.55
6) Find the mean of x and y, if the regression equation are 5x - 2y -4= 0 and 4x - 7y +13= 0. 2, 3
7) The regression equation of y on x is 15x - 4y = 14 and the regression equation of x on y is 7x + 2y= 11. Estimate
A) the value of x when y= 2. 1
B) the value of y when x= 4. 11.5
8) A) If 2y= 3x+ 6 and 3x= 5y +10 be the regression lines of x on y and y on x respectively, find the ratio of variance of x and y. 10:9
B) if the equations of two regression lines are 3x+ 12y= 19 and 3y+ 9x = 46, determine the means of x and y, the correlation coefficient between x and y, the ratio of variances of x and y. 5, 1/3, 1/2√3, 4: 3
C) The lines of regression of y on x on y are respectively y= x+ 5 and 16x = 9y - 94. Find
i) the variance of x if the variance of y is 16. 9
ii) the variance of x and y. 9
D) Two lines of regression are given by x + 2y = 5 and 2x+ 3y= 8 and σ²ₓ= 12. Find
i) mean of x. 1
ii) mean of y. 2
iii) standard deviation of y. 2
iv) r. 0.866
9) Regression equation of two variables x and y are as follows: 3x+ 2y - 26 = 0 and 6x + y -31 = 0. Find
A) the mean of x. 4
B) the regression coefficient of x on y and y. -1/6
C) The coefficient of correlation between x and y. - 0.5
D) the most probable value of y when x= 5. 5.5
10) In a partly destroyed record the following data are available: Variance of x= 25, Regression equation of x upon y is 5x - y = 22 and that of y upon x is 64x - 45y = 25. Find
A) mean value of x and y. 6, 8
B) standard deviation of y. 40/3
C) coefficient of correlation between x on y. 8/15
11) For a bivertia data the mean value of x is 20 and the mean value of y is 45. The regression coefficient of y on x is 4 and that of x on y is 1/9. Find
A) the coefficient of correlation. 2/3
B) the standard deviation of x if the standard deviation of y is 12. 2
C) find the equations of regression lines. y= 4x -35; x= y/9 + 15
12) The coefficient of correlation between the ages of husbands and wives in a community was found to be 0.8; the mean of husband's age was 25 years and that of wives 22 years. Their standard deviations were 4 and 5 years respectively. Find the two lines of regression. Also obtain
A) the expected age of husband when wife's age is 12 years. 19
B) the the expected age of wife when husband's age is 33 years. 30
13) A) A sample of size n= 16 yield the following sums. ∑x= 749, ∑y= 77.90, ∑x² = 42.177, ∑y² = 454.81, ∑xy = 3156.80. Compute the linear regression equation of x on y. x= 78.4 - 6.49 y
B) A sample of size n= 10 yield the following sums. Mean of x = 90, mean of y= 70, ∑x² = 6360, ∑y² = 2860, ∑xy = 3900. Compute the linear regression equations. Y= 0.61X + 15.1, X= 1.36Y - 5.2
14) From the following results, obtain two regression equations and estimate the yield of crops when the rainfall is 22cms, and the rainfall when the yield is 600 kg:-
Y(yield in kg) X(rainfall in cm)
Mean 508.4 26.7
S. D. 36.8 4.6 Coefficient of correlation between yield and rainfall= 0.52. 488.8kg , 32.7 cm
15) You are given the following data:
X Y
Arithmetic mean: 20 25
Standard deviation: 5 4
Correlation coefficient between x on y is 0.6. find the two regression equations. Y= 0.48x +15.4, x= 0.75y + 1.25
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