Advertisements
Advertisements
प्रश्न
The following results were obtained from records of age (X) and systolic blood pressure (Y) of a group of 10 men.
| X | Y | |
| Mean | 50 | 140 |
| Variance | 150 | 165 |
and `sum (x_i - bar x)(y_i - bar y) = 1120`
Find the prediction of blood pressure of a man of age 40 years.
उत्तर
Given, X = Age, Y = Systolic blood pressure,
n = 10, `bar x = 50, bar y = 140,`
`sigma_"X"^2 = 150, sigma_"Y"^2 = 165 and`
`sum (x_i - bar x)(y_i - bar y) = 1120`
Since Var(X) = `(sum (x_i - bar x)^2)/"n"`,
`sigma_"x"^2 = (sum (x_i - bar x)^2)/"n"`
∴ `150 = (sum (x_i - bar x)^2)/10`
∴ `sum (x_i - bar x)^2 = 1500`
Now, `"b"_"YX" = (sum (x_i - bar x)(y_i - bar y))/(sum (x_i - bar x)^2) = 1120/1500 = 0.7`
∴ The regression equaiton of systolic blood pressure of the men (Y) on their age (X) is
`("Y" - bar y) = "b"_"YX" ("X" - bar x)`
∴ (Y - 140) = 0.7(X - 50)
∴ Y - 140 = 0.7X - 35
∴ Y = 0.7X - 35 + 140
∴ Y = 0.7X + 105
For X = 40,
Y = 0.7(40) + 105 = 28 + 105 = 133
∴ The man of age 40 years has systolic blood pressure 133.
APPEARS IN
संबंधित प्रश्न
Bring out the inconsistency in the following:
bYX + bXY = 1.30 and r = 0.75
Bring out the inconsistency in the following:
bYX = 1.9 and bXY = - 0.25
For a certain bivariate data
| X | Y | |
| Mean | 25 | 20 |
| S.D. | 4 | 3 |
And r = 0.5. Estimate y when x = 10 and estimate x when y = 16
Two samples from bivariate populations have 15 observations each. The sample means of X and Y are 25 and 18 respectively. The corresponding sum of squares of deviations from respective means is 136 and 150. The sum of the product of deviations from respective means is 123. Obtain the equation of the line of regression of X on Y.
The following data about the sales and advertisement expenditure of a firms is given below (in ₹ Crores)
| Sales | Adv. Exp. | |
| Mean | 40 | 6 |
| S.D. | 10 | 1.5 |
Coefficient of correlation between sales and advertisement expenditure is 0.9.
Estimate the likely sales for a proposed advertisement expenditure of ₹ 10 crores.
For bivariate data, the regression coefficient of Y on X is 0.4 and the regression coefficient of X on Y is 0.9. Find the value of the variance of Y if the variance of X is 9.
For a bivariate data: `bar x = 53, bar y = 28,` bYX = - 1.5 and bXY = - 0.2. Estimate Y when X = 50.
The equations of two regression lines are x − 4y = 5 and 16y − x = 64. Find means of X and Y. Also, find correlation coefficient between X and Y.
For certain X and Y series, which are correlated the two lines of regression are 10y = 3x + 170 and 5x + 70 = 6y. Find the correlation coefficient between them. Find the mean values of X and Y.
Choose the correct alternative:
If for a bivariate data, bYX = – 1.2 and bXY = – 0.3, then r = ______
Choose the correct alternative:
If the regression equation X on Y is 3x + 2y = 26, then bxy equal to
Choose the correct alternative:
Both the regression coefficients cannot exceed 1
State whether the following statement is True or False:
If byx = 1.5 and bxy = `1/3` then r = `1/2`, the given data is consistent
State whether the following statement is True or False:
If u = x – a and v = y – b then bxy = buv
Corr(x, x) = 1
Arithmetic mean of positive values of regression coefficients is greater than or equal to ______
Given the following information about the production and demand of a commodity.
Obtain the two regression lines:
| Production (X) |
Demand (Y) |
|
| Mean | 85 | 90 |
| Variance | 25 | 36 |
Coefficient of correlation between X and Y is 0.6. Also estimate the demand when the production is 100 units.
For a certain bivariate data of a group of 10 students, the following information gives the internal marks obtained in English (X) and Hindi (Y):
| X | Y | |
| Mean | 13 | 17 |
| Standard Deviation | 3 | 2 |
If r = 0.6, Estimate x when y = 16 and y when x = 10
