Bus 310 Final Exam  2020                                        Name: __________________________________

The study below is evaluating the Revenue ($1000s/week) for Costco. The variables are how many feet in Store (1000 feet increments), Inventory ($1000), Advertising ($1000) Size of District (1 mile increments) Competitors (in 1 unit increments). Randomized data was used for the regression analysis results based on a level of Significance is .05.  Answer the following questions (30 Points): 

R2=0.023

 

1. Write the regression model and equation that estimates sales. Make sure you use all the coefficients listed in the regression analysis. Be sure to define what each variable is including units and their corresponding coefficients.

 

 

 

 

 

 

1. Predict Costco’s expected Revenue would be for a 20,000 foot store $100,000 in inventory, $10,000 in advertising, with a 5 mile district with 2 competitors?

 

 

 

 

1. Set up a hypothesis testing whether there is a significant correlation between Revenue and this set of explanatory variables at the level of significance 0.05. State the appropriate p-value and decide which hypothesis to conclude.

 

 

 

 

 

 

1. Interpret in detail the meaning of the 95% confidence interval of slope for Advertising? Indicate if it is a significant predictor or not. Hint: Look at the confidence interval for the slope. Do not forget about “holding all other variables constant”

 

 

 

 

 

1. Interpret in detail the meaning of the slope for Competition. Comment on how this slope does or does not make sense for the given situation.

 

 

 

 

 

 

1. Discuss how good the model is in terms of variability after adjusting for sample size and amount of variables. Are there enough factors to predict sales accurately?

 

 

 

 

 

1. Does Inventory variable make a significant contribution to the regression model at the level of significance 05? Set up hypotheses and draw conclusion in details including the actual confidence level.

 

 

 

 

 

 

 

 

1. Interpret the slope of Size of district. In particular, discuss the expected effect on Revenue when the district is 10 miles. Do these expected effects make business sense?

 

 

 

 

1. Interpret in detail the intercept for this regression model. Does the intercept have a slope?

 

 

 

 

 

 

2. Is the model valid and reliable? Explain in terms of the validity of the assumptions Be sure to state the general purpose of each assumption, what graph/statistics is used, and what the particular graph/statistics used says about the assumption. Also, state the potential consequences of using this model when a particular assumption is possibly invalid.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CASE STUDIES

For the Next two Cases interpret the results. Include all relevant information such as hypothesis, confidence levels, p-values, and assumptions as applicable, interpretations, etc. Use the format discussed in class and used in the homework.

Case 1: College Majors and gender

In the case below you will determine if there is/are significant dependency/dependencies between job type and gender then state where the dependency is based on the data. The level of significance is at .05.  Answer the Question: What recommendation would you offer to create parity in Business. (25 Points)

Following data was gathered

Observed Frequencies
	Column variable
Row variable	Philosophy	Education	Chemistry	Business	Biology	Agriculture	Engineer	Total
Male	36	33	34	14	18	51	47	233
Female	29	33	23	51	11	3	17	167
Total	65	66	57	65	29	54	64	400
Expected Frequencies
	Column variable
Row variable	Philosophy	Education	Chemistry	Business	Biology	Agriculture	Engineer	Total
Male	37.8625	38.445	33.2025	37.8625	16.8925	31.455	37.28	233
Female	27.1375	27.555	23.7975	27.1375	12.1075	22.545	26.72	167
Total	65	66	57	65	29	54	64	400

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Case 2: Effective Advertisement

You are an Analysis at a marketing Firm. You are conducting research to figure out where is the best location to put an ad in a newspaper. The areas in the newspaper you are investigating is Currents News section, Business Section, and the sports section. The adds include a coupon so you will track the amount of purchases with a coupon. Based on randomized data that is analyzed below, please evaluate the test and write up results.  Include a hypothesis, confidence level, significant difference (in any) and check all assumptions to confirm the results are valid in your write up. The level of significance is at .05. (25 Points) 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A few scenarios follow which require you to choose an appropriate term and test. To refresh your memory some of the terms and tests that you have used include:

1. Intercept                            B. Slope
2. Predicted Y     D. VIF
3. Scatter Diagram F. Correlation
4. R-Squared H. Adjusted R-Squared
5. Standard Error           J.  P-values
6. Assumption of Fit (Linearity)   L. Assumption of Constant Variability
7. Assumption of Normality    N. Normal P-Plot
8. Assumption of Independence P. Durbin-Watson Statistic
9. Relevant range       R. Outlier(s)
10. —————- T. Dummy Variable
11. Multicollinearity V. Interaction

 

For each of the next questions, choose the most appropriate term above that best fits the regression situation. Choose only one and write the letter in the space provided below the question. (5 Points)

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1. You wish to know how strongly correlated are you variables?

 

 

 

 

 

2.         Your VIF is at 15 what is this indicating?

 

 

 

 

 

3. In regression, you want to make sure that the confidence intervals and p-values that you obtain are accurate.

 

 

 

 

4.         There are a few unusual or highly unexpected data points throwing off your regression estimate.

 

 

 

 

5.         What does the Multiple R indicate.

 

 

 

 

 

We have covered various tests and confidence intervals and many of these are listed below. Read the following short scenarios and pick the test or confidence interval that best meets the objective. Choose only one and write the number in the space provided below the question.

1. Confidence interval for a proportion.

2. Confidence interval for a mean

3. Test for a population Proportion

4. Test for comparing Proportions between 2 groups.

5. Test for comparing Proportions between c groups. (c>2)

6. Test for no relationship between 2 categorical variables.

7. Test for a Population Mean

8. Test for Means comparing 2 groups.

9. Test for Means comparing c groups.  (c>2)

10. Tukey-Kramer Procedure for Means.

11. Confidence interval for a slope.

12. Confidence interval for a predicted value of Y.

13. Test for all slopes in a Multiple Regression model.

14. Test for one slope in a Multiple Regression model.

15. Test for one slope in a Simple Regression model.

 

what would you use for the following issues: (5 Points)

Hint: always start by determining what data you have and check if your answer method is appropriate for it

 

6. You want to find out with 95% confidence the Advertisement

 

 

 

7. You suspect a relationship between Inventory and Sales

 

 

 

 

8. You did a marketing survey and collected data on how many men vs women shop at Macys and want test if there is a relationship.

 

 

 

9. You ran an ANOVA and now wish to find out which sample is different what would you use.

 

 

 

 

10. You want to investigate if sales tends to change depending on the amount of advertisement?