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: β2 = 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.
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