General guidelines:
Use EXCEL or PHStat to do the necessary computer work.
Do all the necessary analysis and hypothesis test constructions, and explain completely.
Read the textbook Chapter 13. Imagine that you are managing a mobile phone company. You want to construct a simple linear regression model to capture and represent the relationship between the number of customers and the annual sales level for a year with 95% confidence. You had conducted a pilot study for the past fifteen years and collected yearly observations as given in the following data.Where the number of customers in a year is represented by the Profiled Customers variable, measured by million customers unit, and the sales level is represented by the Annual Sales variable, measured by million US-dollars unit.
1) Investigate the agreement between the model and the data set for:
A) LINEARITY.
A1) Construct the "Dot Plot", a.k.a. "Scatter Plot," for this data. Visually inspect for the linear relationship between the number of customers and the sales level. Make comments based on your observations.
A2) Conduct the F-Test for linearity.
A3) If you have seen evidence of linearity in the F-Test, then:
Conduct the t-Test for the partial slope.
Construct the 95% Confidence Interval Estimator for the partial slope.
Thus, make comments about the linear relationship between the Profiled Customers and the Annual Sales, based on the partial slope information.
B) NORMALITY.
Construct the "Normal Probability Plot" for the Annual Sales variable, and make comments about the normality of annual sales level, based on your observations.
C) HOMOSCEDASTICITY.
Construct the "Residual Plot" and make comments about the variance of annual sales level, based on your observations.
D) INDEPENDENCE.
This data set is a Time-Series. Hence, investigate for the independence of observations in this time-series, based on the Durbin-Watson test.
2) If there is evidence of agreement between the model and data, and independence of observations, then construct the simple linear regression equation for this data set, based on the least square error method.
2A) Construct the 95% confidence interval for the actual average annual sales level for all the years that you have 5 million customer in a year,
2B) Construct the 95% prediction interval for the actual annual sales level for one year that you have 5 million customers in that year.
| Years | Profiled Customers | Annual Sales | |
| 1 | 3.7 | 5.7 | |
| 2 | 3.6 | 5.9 | |
| 3 | 2.8 | 6.7 | |
| 4 | 5.6 | 9.5 | |
| 5 | 3.3 | 5.4 | |
| 6 | 2.2 | 3.5 | |
| 7 | 3.3 | 6.2 | |
| 8 | 3.1 | 4.7 | |
| 9 | 3.2 | 6.1 | |
| 10 | 3.5 | 4.9 | |
| 11 | 5.2 | 10.7 | |
| 12 | 4.6 | 7.6 | |
| 13 | 5.8 | 11.8 | |
| 14 | 2.9 | 4.1 | |
| 15 | 3 | 4.1 |
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Macro Company has the following adjusted accounts and balances at June 30:
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How do you prepare an adjusted trial balance for Macro Company at June 30? |
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