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Applied Mathematics · 2024 · 4 marks
CBSE 2024 · Central · Set 4 · Q38
When observed over a long period of time, a time series data can predict trends that can forecast increase or decrease or stagnation of a variable…
When observed over a long period of time, a time series data can predict trends that can forecast increase or decrease or stagnation of a variable under consideration. Such analytical studies can benefit a business for forecasting or prediction of future estimated sales or production.
The table below shows the sale of an item in a district during $\displaystyle 1996$ – $\displaystyle 2001$ :
| Year : | $\displaystyle 1996$ | $\displaystyle 1997$ | $\displaystyle 1998$ | $\displaystyle 1999$ | $\displaystyle 2000$ | $\displaystyle 2001$ |
| Sales (in lakh ₹) : | $\displaystyle 6.5$ | $\displaystyle 5.3$ | $\displaystyle 4.3$ | $\displaystyle 6.1$ | $\displaystyle 5.6$ | $\displaystyle 7.8$ |
Based on the above information, answer the following questions :
(i)
Determine the equation of the straight-line trend.
(ii)
Tabulate the trend values of the years and also compute expected sales trend for the year 2002.
Fit a straight-line trend by the method of least squares for the following data :
| Year : | $\displaystyle 2004$ | $\displaystyle 2005$ | $\displaystyle 2006$ | $\displaystyle 2007$ | $\displaystyle 2008$ | $\displaystyle 2009$ | $\displaystyle 2010$ |
| Profit (₹ '$\displaystyle 000$) | $\displaystyle 114$ | $\displaystyle 130$ | $\displaystyle 126$ | $\displaystyle 144$ | $\displaystyle 138$ | $\displaystyle 156$ | $\displaystyle 164$ |
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