The document describes two linear regression models created to analyze sales and profit before tax data for Abhinav Technologies over 20 years. The first model for predicting sales had an R^2 of 0.996, indicating the model explained 99.6% of the variability in sales based on material, other incomes, personnel, and interest payments. Only interest payments were not a statistically significant predictor. The second model for predicting profit before tax had an R^2 of 0.934, showing the model explained 93.4% of the variability in profit based on the same predictor variables. Material and interest payments were not statistically significant for this model.

1. STATISTICS
ASSIGNMENT
Group-9
Manish Lahoti- 2014012
Poonam Menaria- 2014020
Harish Beniwal- 2014009

2. Company Name: Abhinav Technologies
Data set period: 20 Years
Response Variable: Sales
Predictor Variable: Other Incomes (OTINC.), Personnel (EMPL), Material (MAT), and Interest payment (INT)
Solution-1
•Regression model Building:
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.998
R Square 0.996
Adjusted R Square 0.995
Standard Error 1675.333
Observations 20
ANOVA
df SS MS F Significance F
Regression 4 10293136486.99 2573284121.748 916.82256 0.00000
Residual 15 42101125.56 2806741.704
Total 19 10335237612.55
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept -10673.815 5236.579 -2.038 0.0596 -21835.319 487.689 -21835.319 487.689
MAT 1.328 0.114 11.696 0.0000 1.086 1.569 1.086 1.569
OTINC 3.008 0.694 4.333 0.0006 1.528 4.487 1.528 4.487
EMPL 0.764 0.323 2.368 0.0317 0.076 1.451 0.076 1.451
INT 2.494 1.321 1.888 0.0785 -0.321 5.309 -0.321 5.309

3. a) Model Presentation
 Linear Regression equation: ŷ = b0 + b1x1 +b2x2 +b3x3 + b4x4
ŷ = -10673.815 + 1.328 MAT + 3.008 OTINC + 0.764 EMPL + 2.494 INT
where: ŷ = Predicted Sales
b0= Intercept
b1, b2, b3, b4= Slope of predictors variable (MAT, OTINC, EMPL & INT respectively)
 Coefficient of Determination R2 = 0.996
 99.6% of total variability of sales is captured by the model.
 R2 is closed to 1 implies that sales are closed to the regression line, thus it is a successful Model and have strong
relationship between response and predictors. Also it explained 99.6% of sales (Dependant variable) by other
variables (independent variable-MAT, OTINC, EMPL & INT)
b) P-Value indicates whether the predictors variables have significant role in the model or not.
If P-Value < 0.05 then the Model is significant.
P-Value of Interest payment (INT) is more than 0.05 thus INT has no significant role in the model.
P-value of MAT, OTINC and EMPL is less than 0.05 thus all these three variables are significant in
explaining the sales.

4. c) Effect of personnel EMPL on sales:
ŷ = -10673.815 + 1.328 MAT + 3.008 ONITC + 0.764 EMPL + 2.494 INT
If, EMPL is increased by 1 unit then sales will increase by 0.764 units, provided MAT, OTINC and
INT expenditure are kept same.
d) Model Usefulness:
Coefficient of Determination R2 gives the goodness of fit of the model.
R2 = 0.996
 99.6% of total variability of sales is captured by the model.
 R2 is closed to 1 means sales is closed to the regression line, thus it is a Useful Model and have strong relationship
between response and predictors. Also it explained 99.6% of sales (Dependant variable) by other variables
(independent variable-MAT, OTINC, EMPL & INT)

5. (a) Regression model Building:
Company Name: Abhinav Technologies
Data set period: 20 Years
Response Variable: Profit before Tax (PBT)
Predictor Variable: Other Incomes (OTINC.), Personnel (EMPL),
Material (MAT), and Interest payment (INT)
Solution-2
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.966
R Square 0.934
Adjusted R Square 0.916
Standard Error 497.304
Observations 20
ANOVA
df SS MS F Significance F
Regression 4 52480724 13120181 53 0.00
Residual 15 3709669 247311
Total 19 56190394
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept -3998.638 1554.420 -2.572 0.021 -7311.806 -685.469 -7311.806 -685.469
MAT -0.029 0.034 -0.853 0.407 -0.101 0.043 -0.101 0.043
OTINC 0.521 0.206 2.530 0.023 0.082 0.961 0.082 0.961
EMPL 0.296 0.096 3.096 0.007 0.092 0.500 0.092 0.500
INT 0.809 0.392 2.062 0.057 -0.027 1.644 -0.027 1.644

6. a) Model Presentation:
Linear Regression equation: ŷ = b0 + b1x1 +b2x2 +b3x3 + b4x4
ŷ = -3998.638 – 0.029 MAT + 0.521 OTINC + 0.296 EMPL + 0.809 INT
where: ŷ = Profit before Tax (PBT)
b0= Intercept
b1, b2, b3, b4= Slope of predictors variable (MAT, OTINC, EMPL & INT respectively)
• Coefficient of Determination R2 = 0.934
• 93.4% of total variability of Profit before Tax (PBT) is captured by the model.
• R2 closed to 1 means Profit before Tax (PBT) is close to the regression line, thus it is a successful Model and have
strong relationship between response and predictors. Also it explained 93.4% of PBT (Dependant variable) by other
variables (independent variable-MAT, OTINC, EMPL & INT)
b) P-Value implies whether the predictors variables have significant role in the model or not.
If P-Value < 0.05 then the Model is significant.
P-Value of Material (MAT) and Interest payment (INT) is more than 0.05 thus MAT & INT has no
significant role in the model.
P-value of OTINC and EMPL is less than 0.05 thus all these three variables are significant in
explaining Profit before Tax (PBT).

7. c) Effect of Interest Payment INT on PBT:
ŷ = -3998.638 – 0.029 MAT + 0.521 OTINC + 0.296 EMPL + 0.809 INT
If, INT is increased by 1 unit then PBT will increase by 0.809 units, provided MAT, OTINC and
EMPL expenditure are kept same.
However, it should be noted that P-value of Interest payment (INT) is more than 0.05 thus INT has
no significant in the model.
d) Model Usefulness:
Coefficient of Determination R2 gives the goodness of fit of the model.
R2 = 0.934
 93.4% of total variability of Profit before Tax (PBT) is captured by the model.
 R2 close to 1 means Profit before Tax (PBT) is close to the regression line, thus it is a Useful Model and have strong
relationship between response and predictors.

8. Thanks