Advertisements
Advertisements
प्रश्न
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 |
Advertisements
उत्तर
| X = xi | Y = yi | xi2 | yi2 | xiyi | |
| 10 | 5 | 100 | 25 | 50 | |
| 12 | 6 | 144 | 36 | 72 | |
| 13 | 7 | 169 | 49 | 91 | |
| 17 | 9 | 289 | 81 | 153 | |
| 18 | 13 | 324 | 169 | 234 | |
| Total | 70 | 40 | 1026 | 360 | 600 |
From the table, we have,
n = 5, Σxi = 70, Σyi = 40, Σxiyi = 600, Σxi2 = 1026, Σyi2 = 360
`barx = (sumx_"i")/"n" = 70/5` = 14, `bary = (sumy_"i")/"n" = 40/5` = 8
Now, for regression equation of X on Y
bxy = `(sumx_"i"y_"i" - "n"bar(x) bar(y))/(sumy_"i"^2 - "n" bar(y)^(-2))`
= `(600 - 5 xx 14 xx 8)/(360 - 5(8)^2)`
= `(600 - 560)/(360 - 320)`
= `40/40`
= 1
Also, a' = `barx - "b"_(xy) bary` = 14 – 1 (8)
= 14 – 8
= 6
∴ The regression equation of X on Y is
X = a' + bxy Y
∴ X = 6 + Y
APPEARS IN
संबंधित प्रश्न
Choose the correct alternative:
There are ______ types of regression equations
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.
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.
From the following data obtain the equation of two regression lines:
| X | 6 | 2 | 10 | 4 | 8 |
| Y | 9 | 11 | 5 | 8 | 7 |
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.
byx = ______
Choose the correct alternative.
bxy = ______
Choose the correct alternative.
If bxy < 0 and byx < 0 then 'r' is __________
Choose the correct alternative.
If equations of regression lines are 3x + 2y − 26 = 0 and 6x + y − 31 = 0 then means of x and y are __________
Fill in the blank:
Regression equation of Y on X 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:
If byx > 1 then bxy is _______
Corr (x, x) = 1
State whether the following statement is True or False.
Corr (x, y) = Corr (y, x)
State whether the following statement is True or False.
bxy and byx are independent of change of origin and scale.
‘r’ is regression coefficient of Y on X
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 ______.
