The following table shows the information as:
| Statistical Measures | Advertisement Expenditure (X) (Rs. Lakhs) | Sales (Y) (Rs Lakhs) |
|---|---|---|
| Mean | 20 | 100 |
| Standard Deviation | 03 | 12 |
. Then find
(i) the expected advertising expenditure of the company if sale is Rs. 125 lakhs, and
(ii) the expected sales of the company if the advertising expenditure is Rs 32 lakhs.
We are given: [ \bar{X} = 20, \quad \bar{Y} = 100, \quad \sigma_X = 3, \quad \sigma_Y = 12, \quad r = 0.8 ] We will use the formulas for regression lines: 1. Regression of (X) on (Y): [ X _________ ______ ____ ________ _____ _______ ___ ______ ______.
______ ______ _______ _______ _____ _____ ________ ______.
____ _________ ___ ________ ______ ___ ______.
___ _________ _____ ______ _____ _______ ______ _______ ____ ________ ____.
_____ ___ _________ __________ ____ ________.
_______ _______ _________ _________ ____ ___.
_________ __________ ______ _______ ______.
_____ ________ ___ ____ ________ __________ __________ __________ ______ _________.
___ _________ ________ _________ ______ ____ ______ ___ ___ ___ ___.
__________ ____ _________ ________ ___ ________ __________ _________ _______ _______ __________.
______ ________ ___ ____ ________ ___ _________ _____ _______ _____ _______.
____ ______ ____ _____ __________ ____ _____ ___ __________.
_________ ______ ___ ______ _______ _____ ___.
____ ____ __________ _____ ____ _____ ________ ____ __________ _____ _______ _____.
_______ _______ _________ _______ __________ _________ __________ ________ ____ _____ _______ _____.
____ ________ ______ ________ __________ ____ _______ ________ ______ _______ ________ ___.
_____ ______ _________ ____ ________ ___ _______ ______ ____ _______ _____ ________.
____.
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Can vaccination be regarded as a preventive measure for smallpox from the given data:
(i) Of 1482 persons in a locality exposed to smallpox, 368 in all were attacked, and
(ii) Of 1482 persons, 343 had been vaccinated and of these only 35 were attacked.
(a) In a statistical study relating to the prices (in T) of two shares, X and Y, the following two regression lines were found as and
. The standard deviation of
, then find (i) the values of X and Y, (ii) r(X, Y), and (iii) standard deviation of Y.
Given the following data: ,
and
then find (i) r12.3 (ii) r13.2 (iii) r23.1 (iv) R1.23
Calculate Karl Pearson's coefficient of correlation between X and Y for the following data: and
.
The value of Spearman's rank correlation coefficient of a set of non-repeating values was found to be 2/3. The sum of the squares of difference between the corresponding ranks was 55. Find the number of pairs.
Suppose X and Y are the two variables having the correlation coefficient 0.85. The following are the values they have:
| X | Y |
|---|---|
| 10 | 40 |
| 30 | 30 |
| 50 | 70 |
| 60 | 80 |
State whether the following statements are true or false and also give the reason in support of your answer:
(a) If and
are the variate values of two variables X and Y, and their geometric means are G1 and G2, respectively, then geometric mean of
will be (G1/G2).
(b) If X and Y are two independent variables and the variables and
, then the
(c) If each value of X is divided by 2 and of Y is multiplied by 2, then b'YX will be same as b.
(d) The mean and standard deviation of a set of values are 25 and 5, respectively. If a constant value 5 is added to each value, the coefficient of variation of the new set of values is equal to 10%.
(e) If and
then
.