Advertisements
Advertisements
Question
From the following data estimate y when x = 125.
| X | 120 | 115 | 120 | 125 | 126 | 123 |
| Y | 13 | 15 | 14 | 13 | 12 | 14 |
Solution
In order to estimate y, we have to find the regression equation of Y on X.
| X = xi | Y = yi | `"x"_"i"^2` | xi yi |
| 120 | 13 | 14400 | 1560 |
| 115 | 15 | 13225 | 1725 |
| 120 | 14 | 14400 | 1680 |
| 125 | 13 | 15625 | 1625 |
| 126 | 12 | 15876 | 1512 |
| 123 | 14 | 15129 | 1722 |
| 729 | 81 | 88655 | 9824 |
From table, we get
n = 6, ∑ xi = 729, ∑ yi = 81, ∑ `"x"_"i"^2` = 88655, ∑ xi yi = 9824
∴ `bar"x" = (sum "x"_"i")/"n" = 729/6 = 121.5`
∴ `bar"y" = (sum "y"_"i")/"n" = 81/6 = 13.5`
Now,
`"b"_"YX" = (sum"x"_"i" "y"_"i" - "n" bar "x" bar "y")/(sum "x"_"i"^2 - "n" bar"x"^2)`
`= (9824 - 6 xx 121.5 xx 13.5)/(88655 - 6(121.5)^2)`
`= (9824 - 9841.5)/(88655 - 88573.5)`
= `(- 17.5)/81.5`
= - 0.22
Also, `"a" = bar"y" - "b"_"YX" bar"x"`
= 13.5 - (- 0.22) × 121.5
= 13.5 + 26.73
= 40.23
∴ The regression equation of Y on X is
Y = a + bYX X
∴ Y = 40.23 - 0.22 X
For X = 125,
Y = 40.23 - 0.22 × 125 = 40.23 - 27.5 = 12.73
∴ The estimated value of Y is 12.73 for X = 125.
APPEARS IN
RELATED QUESTIONS
Choose the correct alternative:
There are ______ types of regression equations
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 |
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 |
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.
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 = ______
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 bxy = _______
Fill in the blank:
If u = `"x - a"/"c" and "v" = "y - b"/"d"` then 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
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 |
