Advertisements
Advertisements
प्रश्न
Compute the appropriate regression equation for the following data:
| X [Independent Variable] |
2 | 4 | 5 | 6 | 8 | 11 |
| Y [dependent Variable] | 18 | 12 | 10 | 8 | 7 | 5 |
Advertisements
उत्तर
Since X is independent and Y is dependent variable, we find the regression equation of Y on X.
| X = xi | Y = yi | `"x"_"i"^2` | xi yi |
| 2 | 18 | 4 | 36 |
| 4 | 12 | 16 | 48 |
| 5 | 10 | 25 | 50 |
| 6 | 8 | 36 | 48 |
| 8 | 7 | 64 | 56 |
| 11 | 5 | 121 | 55 |
| 36 | 60 | 266 | 293 |
From the table, we have,
n = 6, ∑ xi = 36, ∑ yi = 60, `sum "x"_"i"^2 = 266`, ∑ xi yi = 293
`bar"x" = (sum "x"_"i")/"n" 36/6 = 6`
`bar"y" = (sum "y"_"i")/"n" = 60/6 = 10`
Now, `"b"_"YX" = (sum"x"_"i" "y"_"i" - "n" bar "x" bar "y")/(sum "x"_"i"^2 - "n" bar"x"^2)`
`= (293 - 6xx6xx10)/(266 - 6(6)^2) = (293 - 360)/(266 - 216) = (-67)/50`
∴ bYX = - 1.34
Also, `"a"' = bar"y" - "b"_"YX" bar"x"`
= 10 - (- 1.34)(6) = 10 + 8.04 = 18.04
The regression equation of Y on X is
Y = a + bYX X
∴ Y = 18.04 - 1.34 X
APPEARS IN
संबंधित प्रश्न
Choose the correct alternative:
There are ______ types of regression equations
The HRD manager of a company wants to find a measure which he can use to fix the monthly income of persons applying for the job in the production department. As an experimental project, he collected data of 7 persons from that department referring to years of service and their monthly incomes.
| Years of service (X) | 11 | 7 | 9 | 5 | 8 | 6 | 10 |
| Monthly Income (₹ 1000's)(Y) | 10 | 8 | 9 | 5 | 9 | 7 | 11 |
- Find the regression equation of income on years of service.
- What initial start would you recommend for a person applying for the job after having served in a similar capacity in another company for 13 years?
Calculate the regression equations of X on Y and Y on X from the following data:
| X | 10 | 12 | 13 | 17 | 18 |
| Y | 5 | 6 | 7 | 9 | 13 |
The following table gives the aptitude test scores and productivity indices of 10 workers selected at random.
| Aptitude score (X) | 60 | 62 | 65 | 70 | 72 | 48 | 53 | 73 | 65 | 82 |
| Productivity Index (Y) | 68 | 60 | 62 | 80 | 85 | 40 | 52 | 62 | 60 | 81 |
Obtain the two regression equations and estimate the productivity index of a worker whose test score is 95.
The following table gives the aptitude test scores and productivity indices of 10 workers selected at random.
| Aptitude score (X) | 60 | 62 | 65 | 70 | 72 | 48 | 53 | 73 | 65 | 82 |
| Productivity Index (Y) | 68 | 60 | 62 | 80 | 85 | 40 | 52 | 62 | 60 | 81 |
Obtain the two regression equations and estimate the test score when the productivity index is 75.
From the following data, find the regression equation of Y on X and estimate Y when X = 10.
| X | 1 | 2 | 3 | 4 | 5 | 6 |
| Y | 2 | 4 | 7 | 6 | 5 | 6 |
The following sample gives the number of hours of study (X) per day for an examination and marks (Y) obtained by 12 students.
| X | 3 | 3 | 3 | 4 | 4 | 5 | 5 | 5 | 6 | 6 | 7 | 8 |
| Y | 45 | 60 | 55 | 60 | 75 | 70 | 80 | 75 | 90 | 80 | 75 | 85 |
Obtain the line of regression of marks on hours of study.
Choose the correct alternative.
Corr (x, x) = _____
Choose the correct alternative.
byx = ______
Choose the correct alternative.
Cov (x, y) = __________
Fill in the blank:
If bxy < 0 and byx < 0 then ‘r’ is __________
Fill in the blank:
If u = `"x - a"/"c" and "v" = "y - b"/"d"` then byx = _______
Fill in the blank:
|bxy + byx| ≥ ______
Fill in the blank:
bxy . byx = _______
Corr (x, x) = 1
State whether the following statement is True or False.
bxy and byx are independent of change of origin and scale.
State whether the following statement is True or False.
byx is correlation coefficient between X and Y
State whether the following statement is True or False.
If u = x - a and v = y - b then rxy = ruv
State whether the following statement is True or False:
Correlation analysis is the theory of games
Compute the appropriate regression equation for the following data:
| x (Dependent Variable) | 10 | 12 | 13 | 17 | 18 |
| y (Independent Variable) | 5 | 6 | 7 | 9 | 13 |
If bxy < 0 and byx < 0 then 'r ' is ______.
