Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
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 test score when the productivity index is 75.
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.
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"_"yx"` = _________
Choose the correct alternative.
Corr (x, x) = _____
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:
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 byx = _______
Fill in the blank:
If byx > 1 then bxy is _______
Fill in the blank:
bxy . byx = _______
Corr (x, x) = 1
Regression equation of X on Y 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.
byx is correlation coefficient between X and Y
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 |
