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Relevant Built-In Function in Excel to Estimate a Simple Linear Regression Model

a.

Regression Model:

Y = β1 + β2X

Where,

Sales Revenue = β1 + β2 Training Hours

The above model depicts that Sales revenue is the dependent variable and Training hours is the independent variable.

SUMMARY OUTPUT

         

Regression Statistics

         

Multiple R

1

         

R Square

1

         

Adjusted R Square

1

         

Standard Error

4.5823E-11

         

Observations

42

         

ANOVA

           

 

df

SS

MS

F

Significance F

 

Regression

1

7.222E+10

7.222E+10

3.4395E+31

0

 

Residual

40

8.3989E-20

2.0997E-21

     

Total

41

7.222E+10

 

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

60000

1.6952E-11

3.5394E+15

0

60000

60000

Hours of Training (x)

15000

2.5577E-12

5.8647E+15

0

15000

15000

b.

Regression line:

Sales Revenue = 6000+ 15000 Training Hours

The value of intercept (β1) in the regression line is equivalent to 60000 and the value of the coefficient of X is equivalent to 15000.  The above computed regression summary has been performed at 90% confidence intervals which indicates that the researcher can be 90% confident that the estimates computed using sample data are true for the population parameter.

The value of the coefficient of X depicts that one unit change in the training hours will increase the sales revenue by 15000 units. The value of the intercept depicts that if there will be no change or 0 unit changes in the training hours still the sales revenue will increase by 6000 units because there must be many other factors impacting sales revenue other than the training hours provided to the new marketers.

c.

Confidence interval for coefficient of X (β2)

Lower limit: β2 – (2.58 ×( Standard Error of β2))

Upper limit: β2 +(2.58 ×( Standard Error of β2))

Lower limit: 15000 – (2.58×4.5823E-11)

Lower limit: 15000

Upper limit: 15000 + (2.58×4.5823E-11)

Upper Limit: 15000

The population parameter of β2 is equivalent to 15000. Therefore, it can be evaluated that the sample estimate is reflecting the true value of the population parameter.

d.

Hypothesis Testing

First step in hypothesis testing is setting up the alternate and null hypothesis

HO: β= 0

HA: β2 > 0

Computing the statistic

Z = 15000-0/4.5823E-11

Z = 3.2734653e+14

The critical value of Z at 0.05 significance level and n equal to 42 is 0.5199. If the computed value of Z will be greater than the 0.5199, then the null hypothesis will be rejected and if the computed value will be less than critical value of z, null hypothesis will be accepted (List et al., 2019). In the above calculation it can be evaluated that critical value of Z is less than the computed value of Z, therefore null hypothesis will be rejected and alternate hypothesis will be accepted.

e.

The value of coefficient of determination value ( r 2 ) is an indicator of the strength of the model. If the value of the coefficient of determination is close to 1 it depicts high strength of model whereas if the value of the coefficient of determination is significantly less than 1 depicts weakness of the model (Taylor, 1990). High strength of the model depicts that most of the changes in dependent variable can be explained with the changes in the independent variable. In the above regression summary, the value of the coefficient of determination value is equal to 1 which depicts a good fit model that most of the changes in the revenue can be explained by the changes in the training hours provided by the marketers.

References

List, J. A., Shaikh, A. M., & Xu, Y. (2019). Multiple hypothesis testing in experimental economics. Experimental Economics, 22(4), 773-793.

Taylor, R. (1990). Interpretation of the correlation coefficient: a basic review. Journal of diagnostic medical sonography, 6(1), 35-39.

Remember, at the center of any academic work, lies clarity and evidence. Should you need further assistance, do look up to our Economics Assignment Help

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