Regression
Ranbaxy Laboratories Ltd, incorporated in 1961, is one of india's largest pharmaceutical companies, Following table exhibits the sales volume & advertisement expenditure (in million rupees) of Ranbaxy Laboratories Ltd from 1989-1990 to 2006-2007
| Year | Sales (In million rupees). | Advertisement (In million rupees). | 
| 1989-1990 | 2064.5 | 30.4 | 
| 1990-1991 | 2587.8 | 51 | 
| 1991-1992 | 3396.9 | 59.1 | 
| 1992-1993 | 4622.2 | 79.5 | 
| 1993-1994 | 5944.7 | 50.8 | 
| 1994-1995 | 7139.2 | 98.2 | 
| 1995-1996 | 8940.1 | 112.7 | 
| 1996-1997 |   10,427.3 | 141.6 | 
| 1997-1998 |   12,421.3 | 224.8 | 
| 1998-1999 |   11,296.5 | 169.8 | 
| 1999-2000 |   16.670.3  | 409.3 | 
| 2000-2001 |   17,757.1 | 560.2 | 
| 2001-2002 |   19.597.8. | 863.5 | 
| 2002-2003 |   31,317.6 | 1306.5 | 
| 2003-2004 |   38,889.8 | 1822.6 | 
| 2004--2005 |  38658.7 | 2017.2 | 
| 2005-2006 |   32,840.3 | 2008.1 | 
| 2006-2007 |   35,991.5 | 1487.1 | 
Regression was run on MS Excel and the partial result below was extracted from the Excel result..
| SUMMARY OUTPUT |   |   |   | 
| 
 |   |   |   |   | 
| Regression   Statistics |   |   |   |   | 
| Multiple   R | 0.9672348 |   |   |   | 
| R   Square | 0.9355432 |   |   |   | 
| Adjusted   R Square | 0.9315146 |   |   |   | 
| Standard   Error | 3430.2371 |   |   |   | 
| Observations | 18 |   |   |   | 
|   |   |   |   |   | 
| ANOVA |   |   |   |   | 
|   | df | SS |   |   | 
| Regression | 1 | 2732519348 |   |   | 
| Residual | 16 | 188264427.6 |   |   | 
| Total | 17 | 2920783775 |   |   | 
|   |   |   |   |   | 
|   | Coefficients | Standard Error | T Stat | Lower    Upper 95%       95% | 
| Intercept | 5794.29 | 1079.85324 | 5.3668 |    3506. 8083 | 
| advertisement | 17.0779 | 1.12067000 | 15.239 |    14.70 19.46 | 
By using the results above & α=0.05, develop a regression model to predict sales from advertisement expenses incurred by performing the following steps.
- State      the linear relationship between sales & advertisement & interpret      the coefficients.
- Obtain      the coefficient of determination & interpret it.
- Obtain      the standard error of estimate & interpret it.
- Comment      on the t test for the slope of the regression line using confidence      interval
- Predict      sales when advertisement is 3000 million rupees