Advertisements
Advertisements
Question
From the following data obtain the equation of two regression lines:
| X | 6 | 2 | 10 | 4 | 8 |
| Y | 9 | 11 | 5 | 8 | 7 |
Advertisements
Solution
| X = xi | Y = yi | `"x"_"i"^2` | `"y"_"i"^2` | xi yi |
| 6 | 9 | 36 | 81 | 54 |
| 2 | 11 | 4 | 121 | 22 |
| 10 | 5 | 100 | 25 | 50 |
| 4 | 8 | 16 | 64 | 32 |
| 8 | 7 | 64 | 49 | 56 |
| 30 | 40 | 220 | 340 | 214 |
From the table, we have
n = 5, ∑ xi = 30, ∑ yi = 40, `sum "x"_"i"^2 = 220`, `sum "y"_"i"^2 = 340,` ∑ xi yi = 214
`bar x = (sum x_i)/"n" = 30/5 = 6`
`bar y = (sum y_i)/"n" = 40/5 = 8`
Now, for regression equation of Y on X,
`"b"_"YX" = (sum"x"_"i" "y"_"i" - "n" bar "x" bar "y")/(sum "x"_"i"^2 - "n" bar"x"^2)`
`= (214 - 5xx 6 xx 8)/(220 - 5(6)^2) = (214 - 240)/(220 - 180) = (-26)/40` = - 0.65
Also, `"a" = bar y - "b"_"YX" bar x`
= 8 - (- 0.65)(6) = 8 + 3.9 = 11.9
The regression equation of Y on X is
Y = a + bYX X
∴ Y = 11.9 - 0.65X
Now, for regression equation of X on Y,
`"b"_"XY" = (sum"x"_"i" "y"_"i" - "n" bar "x" bar "y")/(sum "y"_"i"^2 - "n" bar"y"^2)`
`= (214 - 5 xx 6 xx 8)/(340 - 5(8)^2) = (214 - 240)/(340 - 320) = (-26)/20` = - 1.3
Also, `"a"' = bar x - "b"_"XY" bar y`
= 6 - (- 1.3)8 = 6 + 10.4 = 16.4
The regression equation of Y on X is
X = a' + bXY Y
∴ X = 16.4 - 1.3Y
APPEARS IN
RELATED QUESTIONS
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.
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 |
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.
For the following data, find the regression line of Y on X
| X | 1 | 2 | 3 |
| Y | 2 | 1 | 6 |
Hence find the most likely value of y when x = 4.
Choose the correct alternative.
If u = `("x - a")/"c" and "v" = ("y - b")/"d" "then" "b"_"xy"` = _________
Choose the correct alternative.
Corr (x, x) = _____
Choose the correct alternative.
byx = ______
Choose the correct alternative.
If bxy < 0 and byx < 0 then 'r' is __________
Fill in the blank:
Regression equation of Y on X is_________
Fill in the blank:
There are __________ types of regression equations.
Fill in the blank:
If u = `"x - a"/"c" and "v" = "y - b"/"d"` then bxy = _______
Fill in the blank:
|bxy + byx| ≥ ______
Corr (x, x) = 1
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.
bxy and byx are independent of change of origin and scale.
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
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 |
