Advertisements
Advertisements
प्रश्न
The following are the marks obtained by the students in Economics (X) and Mathematics (Y)
| X | 59 | 60 | 61 | 62 | 63 |
| Y | 78 | 82 | 82 | 79 | 81 |
Find the regression equation of Y on X.
Advertisements
उत्तर
X = Marks obtained in Economics
Y = Marks obtained in Mathematics
| X = xi | Y = yi | `"x"_"i"^2` | xi yi |
| 59 | 78 | 3481 | 4602 |
| 60 | 82 | 3600 | 4920 |
| 61 | 82 | 3721 | 5002 |
| 62 | 79 | 3844 | 4898 |
| 63 | 81 | 3969 | 5103 |
| 305 | 402 | 18615 | 24525 |
From the table, we have
n = 5, ∑ xi = 305, ∑ yi = 402, `sum "x"_"i"^2 = 18615`, ∑ xi yi = 24525
`bar"x" = (sum "x"_"i")/"n" = 305/5 = 61`
`bar"y" = (sum "y"_"i")/"n" = 402/5 = 80.4`
Now, `"b"_"YX" = (sum"x"_"i" y_"i" - "n" bar "x" bar "y")/(sum "x"_"i"^2 - "n" bar"x"^2)`
`= (24525 - 5 xx 61 xx 80.4)/(18615 - 5(61)^2)`
`= (24525 - 24522)/(18615 - 18605) = 3/10` = 0.3
Also, `"a" = bar"y" - "b"_"YX" bar"x"`
= 80.4 - (0.3)(61) = 80.4 - 18.3 = 62.1
The regression equation of Y on X is
Y = a + bYX X
∴ Y = 62.1 + 0.3 X
APPEARS IN
संबंधित प्रश्न
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 |
From the following data estimate y when x = 125.
| X | 120 | 115 | 120 | 125 | 126 | 123 |
| Y | 13 | 15 | 14 | 13 | 12 | 14 |
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.
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 |
From the following data obtain the equation of two regression lines:
| X | 6 | 2 | 10 | 4 | 8 |
| Y | 9 | 11 | 5 | 8 | 7 |
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.
If u = `("x - a")/"c" and "v" = ("y - b")/"d" "then" "b"_"xy"` = _________
The regression equation of y on x is given by 3x + 2y − 26 = 0. Find byx.
Choose the correct alternative.
bxy = ______
Choose the correct alternative.
Cov (x, y) = __________
Choose the correct alternative.
If bxy < 0 and byx < 0 then 'r' is __________
Fill in the blank:
There are __________ types of regression equations.
Fill in the blank:
|bxy + byx| ≥ ______
Fill in the blank:
bxy . byx = _______
State whether the following statement is True or False.
Regression equation of Y on X is `("y" - bar "y") = "b"_"yx" ("x" - bar "x")`
State whether the following statement is True or False.
Corr (x, y) = Corr (y, x)
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 bxy = buv
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
If bxy < 0 and byx < 0 then 'r ' is ______.
