Using the method ofleast squares, fit a straight line trend for Σx = 10, Σy = 16.9, Σx² = 30, Σxy = 47.4 and n = 7.

Calculate the 3-yearlymoving averages of the production figures (in tonnes) for the following data.

Year	1973	1974	1975	1976	1977	1978	1979	1980	1981	1982	1983	1984	1985	1986	1987
Production	15	21	30	36	42	46	50	56	63	70	74	82	90	95	102

Calculate the seasonal indices by the method of simple average for the following data.

Year	I quarter	II quarter	III quarter	IV quarter
1985	68	62	61	63
1986	65	58	66	61
1987	68	63	63	67

Calculate the cost of living index by aggregate expenditure method

Commodity	Quantity	Price(Rs.)
	2000	2000	2003
A	100	8	12
B	25	6	7.50
C	10	5	5.25
D	20	48	52
E	65	15	16.50
F	30	19	27.00

Construct the cost of living index for 2003 on the basis of 2000 from the following data using family budget method.

Item	Price(Rs.)		Weights
Food	2000	2003	30
Rent	200	280	30
Clothing	150	120	20
Fuel & lighting	50	100	10
Miscellaneous	100	200	20

The following data shows the value of sample mean (\(\bar{X}\)) and the range R for 10 samples of size 5 each. Calculate the control limits for : mean chart and range chart.

Sample No.	1	2	3	4	5	6	7	8	9	10
Mean \(\bar{X}\)	11.2	11.8	10.8	11.6	11.0	9.6	10.4	9.6	10.6	10.0
Range	7	4	8	5	7	4	8	4	7	9

(Given for n = 5, A₂ = .577, D₃ = 0, D₄ = 2.115)

Fit a trend line by the method of semi averages

Year	1980	1981	1982	1983	1984	1985	1986
Sales	102	105	114	110	108	116	112

From the data given below calculate seasonal indices.

Year	I Quarter	II Quarter	III Quarter	Iv Quarter
1985	68	62	61	63
1986	65	58	66	61
1987	68	63	63	67

Fit a trend line by method of semi averages. 

Year	1987	1988	1989	1990	1991	1992	1993
Production (in tonnes)	90	110	130	150	100	150	200

Below are given figures of production (in thousand tonnes) of a sugar factory. Obtain the trend values by 3 year moving average.

Year	1980	1981	1982	1983	1984	1985	1986
Production	80	90	92	83	94	99	92

Calculate the seasonal index by the method of simple average for the following data.

Year	I Quarter	II Quarter	III Quarter	Iv Quarter
1985	65	60	61	63
1986	68	55	66	61
1987	68	60	63	67

Fit a straight line to the following \(\Sigma \mathrm{I}=10, \Sigma Y=19, \Sigma \mathrm{X}^{2}=30, \Sigma \mathrm{XY}=53\) and n = 5

In a straight line of best fit find x-intercept when \(\Sigma X=10, \Sigma Y=16.9, \Sigma X^{2}=30, \Sigma X Y=47.4\) n = 7

Fit the line of best fit if \(\Sigma X=75, \Sigma Y=115\), \(\Sigma \mathrm{X}^{-2}=1375, \Sigma X Y=1875\) and n = 6.

In a line of best fit, find the slope and y intercept if \(\Sigma X=10, \Sigma Y=25, \Sigma X^{2}=35, \Sigma X Y=90\) and n = 5.