Advertisements
Advertisements
Question
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.
Advertisements
Solution
| X = xi | Y = yi | `bb("x"_"i"^2)` | xi yi |
| 3 | 45 | 9 | 135 |
| 3 | 60 | 9 | 180 |
| 3 | 55 | 9 | 165 |
| 4 | 60 | 16 | 240 |
| 4 | 75 | 16 | 300 |
| 5 | 70 | 25 | 350 |
| 5 | 80 | 25 | 400 |
| 5 | 75 | 25 | 375 |
| 6 | 90 | 36 | 540 |
| 6 | 80 | 36 | 480 |
| 7 | 75 | 49 | 525 |
| 8 | 85 | 64 | 680 |
| 59 | 850 | 319 | 4370 |
From the table, we have
n = 12, ∑ xi = 59, ∑ yi = 850, `sum "x"_"i"^2 = 319`, ∑ xi yi = 4370
`bar x = (sum x_i)/"n" = 59/12 = 4.92`
`bar y = (sum y_i)/"n" = 850/12 = 70.83`
Now, `"b"_"YX" = (sum"x"_"i" "y"_"i" - "n" bar "x" bar "y")/(sum "x"_"i"^2 - "n" bar"x"^2)`
`= (4370 - 12 xx 4.92 xx 70.83)/(319 - 12 xx (4.92)^2)`
`= (4370 - 4181.80)/(319 - 290.48)`
`= 188.2/28.52` = 6.6
Also, `"a" = bar y - "b"_"YX" bar x`
= 70.83 - 6.6 × 4.92
= 70.83 - 32.47
= 38.36
∴ The regression equation of Y on X is,
Y = a + bYX X
∴ Y = 38.36 + 6.6 X
APPEARS IN
RELATED QUESTIONS
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 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, 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 |
Choose the correct alternative.
If u = `("x - a")/"c" and "v" = ("y - b")/"d" "then" "b"_"yx"` = _________
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.
Cov (x, y) = __________
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:
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:
Corr (x, −x) = __________
Fill in the blank:
If u = `"x - a"/"c" and "v" = "y - b"/"d"` then bxy = _______
Fill in the blank:
If u = `"x - a"/"c" and "v" = "y - b"/"d"` then byx = _______
Fill in the blank:
If byx > 1 then bxy is _______
Fill in the blank:
bxy . byx = _______
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.
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:
Correlation analysis is the theory of games
If bxy < 0 and byx < 0 then 'r ' is ______.
