Q2. The following data show the cost of living indices for different groups along with their weights (% of expenditure), for middle-class people of some city in 2010. Obtain the general cost of living index number. Mr. X was getting a salary of ₹ 25,000 in 2010 and ₹ 82,900 in 2016. Calculate how much he ought to have received as extra allowance in 2016 to maintain his same standard of living.
(a) Group Base year group index Weight Food 396 71.3 Clothing 550 2.7 Fuel and Light 360 9.3 House rent 110 6.7 Miscellaneous 290 10
(b) A simple random sample of 25 households was drawn from a city area containing 13745 households. The number of persons per household in the sample were as follows : 5, 6, 3, 4, 2, 3, 3, 3, 4, 4, 3, 2, 7, 4, 7, 6, 4, 4, 1, 4, 3, 4, 5, 6, 3. Estimate the total number of people in the area and also compute the variance of the estimate.
(c) Discuss the concept of heteroscedasticity. Explain this by graphical representation. Show that OLS estimators are unbiased even under the condition of heteroscedasticity. Obtain its variance.
