Advertisements
Advertisements
प्रश्न
The following data relate to advertisement expenditure (in lakh of rupees) and their corresponding sales (in crores of rupees)
| Advertisement expenditure | 40 | 50 | 38 | 60 | 65 | 50 | 35 |
| Sales | 38 | 60 | 55 | 70 | 60 | 48 | 30 |
Estimate the sales corresponding to advertising expenditure of ₹ 30 lakh.
Advertisements
उत्तर
| X | Y | X2 | Y2 | XY |
| 40 | 38 | 1600 | 1444 | 1520 |
| 50 | 60 | 2500 | 3600 | 3000 |
| 38 | 55 | 1444 | 3025 | 2090 |
| 60 | 70 | 3600 | 4900 | 4200 |
| 65 | 60 | 4225 | 3600 | 3900 |
| 50 | 48 | 2500 | 2304 | 2400 |
| 35 | 32 | 1225 | 900 | 1050 |
| 338 | 361 | 17094 | 19773 | 18160 |
N = 7, ΣX = 338, ΣY = 361, ΣX2 = 17094, ΣY2 = 19773, ΣXY = 18160.
`bar"X" = (sum"X")/"N" = 338/7` = 48.29
`bar"Y" = (sum"Y")/"N" = 361/7` = 51.57
byx = `("N"sum"XY" - (sum"X")(sum"Y"))/("N"sum"X"^2 - (sum"X")^2)`
= `(7(18160) - (388)(361))/(7(17094) - (338)^2)`
= `(127120 - 122018)/(119658 - 114244)`
= `5102/5414`
= 0.942
Regression equation of Y on X
`"Y" - bar"Y" = "b"_"yx"("X" - bar"X")`
Y – 51.57 = 0.942(X – 48.29)
Y – 51.57 = 0.942X – 0.942 × 48.29
Y – 51.57 = 0.942X – 45.48918
Y = 0.942X + 51.57 – 48.29
Y = 0.942X + 6.081
To find the sales, when the advertising is X = ₹ 30 lakh in the above equation we get,
Y = 0.942(30) + 6.081
= 28.26 + 6.081
= 34.341
= ₹ 34.34 crores
APPEARS IN
संबंधित प्रश्न
From the data given below:
| Marks in Economics: | 25 | 28 | 35 | 32 | 31 | 36 | 29 | 38 | 34 | 32 |
| Marks in Statistics: | 43 | 46 | 49 | 41 | 36 | 32 | 31 | 30 | 33 | 39 |
Find
- The two regression equations,
- The coefficient of correlation between marks in Economics and Statistics,
- The mostly likely marks in Statistics when the marks in Economics is 30.
Obtain the two regression lines from the following data N = 20, ∑X = 80, ∑Y = 40, ∑X2 = 1680, ∑Y2 = 320 and ∑XY = 480.
For 5 observations of pairs of (X, Y) of variables X and Y the following results are obtained. ∑X = 15, ∑Y = 25, ∑X2 = 55, ∑Y2 = 135, ∑XY = 83. Find the equation of the lines of regression and estimate the values of X and Y if Y = 8; X = 12.
The equations of two lines of regression obtained in a correlation analysis are the following 2X = 8 – 3Y and 2Y = 5 – X. Obtain the value of the regression coefficients and correlation coefficients.
The regression coefficient of X on Y
When one regression coefficient is negative, the other would be
If X and Y are two variates, there can be at most
The lines of regression intersect at the point
The term regression was introduced by
The following data pertains to the marks in subjects A and B in a certain examination. Mean marks in A = 39.5, Mean marks in B = 47.5 standard deviation of marks in A = 10.8 and Standard deviation of marks in B = 16.8. coefficient of correlation between marks in A and marks in B is 0.42. Give the estimate of marks in B for the candidate who secured 52 marks in A.
