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