Ryder case

Questions

· Linear Regression

STEPS:

1. Identifying the business analysis questions

2. Converting business questions into statistical questions

3. Performing a descriptive analysis of the data

4. Applying formal analysis procedures

5. Developing conclusions and recommendations

6. Identifying unusual outcomes and future analysis

Sections:

· Executive Summary: 1-3 paragraphs, ** Last part written *** identify the problem, indicate your approach to solving it and concisely state conclusion

· Introduction: ~1 Paragraph, intro to the case, project scope.

· BODY: indicate how you developed your conclusions and recommendations

· Part 1: Begin with concise presentation of the question from the business perspective and explain how you conducted the analysis

· Part 2: Define the data set and specify the statistical procedures used

· Include specific statements of statistical models and hypothesis tests

· Results: Discuss the statistical results, indicating how they provide a solution to the case problem

· Include additional observations and extensions of your results

· Identify unusual outcomes, go into detail on the unexplored questions in the study (Questions for future work), might be important enough to justify another study.

· Document the additional questions and suggest how they might be answered and decide whether or not additional work should be taken

· Conclusion

First thing we’re answering:

1. Does the square footage estimates that are already in the database (REC SQRT) differ significantly from the actual data taken in the sample of 80? AKA can we use the already recorded data to decide the tax rate, or do we need to re-measure all the houses with the RAD appraisers (which they may not have the money/resources to do); aka does the Bradford need to send out the RAD appraisers to re- measure all properties, or are the already recorded ones good enough?

(team: don’t use this image in the report, its not necessary, its all explained below.

When performing a t-test, our null hypothesis is that the actual square footage of the properties is statistically equivalent to the measurements already recorded in the database. Our alternative hypothesis is that there is a significant different between the measures. If we reject the null hypothesis, it means that all houses will have to be re-measured. When performing the t-test, we get a P value of .65. means that we do not reject the null and we do not need to re-measure all houses, and we can just use the recorded square footage already in the database. Now, to figure out what the new tax system should be, we are going to use the the recorded square footage data to come to a conclusion.

Second thing we’re answering:

2. Use the sample to estimate the flat tax and tax rate per square foot that should be charged

Dependent variable: tax

Independent variable: recorded square footage

Looking for a formula: tax paid = slope * recorded square footage + y intercept

Before figuring this out, we have to keep in mind that the data given to us gives the taxes paid per property with the discounts factored in. The 10% reduction if the owner lives in the house, and the 10% reduction if the owner is retired must be removed from the data in order to figure out the correct tax rate formula. In addition, when doing the analysis we removed the 3 data points of the unimproved properties. After removing the three unimproved properties, we are able to create a new tax equation, by running a simple linear regression model comparing the original tax amounts (values before the 10% is reduced for the both the homestead exemption and retired owner reduction), and the square footage as recorded in the data base.

Team: I’m thinking we should also explain the meaning of the R-squared value is if someone can figure it out.

The new formula found is Tax = 208.03 + 0.556(Recorded Square Footage). Therefore, the flat tax is $208.03, and the variable component is 0.556 times the recorded square footage. We then figure out everyone’s owed tax amount based on this formula. The new tax plan is maintaining the process of reducing the tax by 10% if the owners live on the property, and 10% if the wonder is retired, so after plugging each square footage into the formula we reduce taxes for those who meet those qualifications. Now, Bradford also did not want his new tax to change people’s individuals tax amount too much, or to significantly change the total amount of tax collected (revenue neutral). To make sure individual tax amounts did not change too much, we run a paired t-test between the new tax amount and old tax amount, using an alpha of .05. Null hypothesis is that the means of the two data sets are equal. Alternative hypothesis is that the means of the two data sets are not equal.

Because the P value of the two tail test is .846, higher than the alpha value, we fail to reject the null hypothesis, and conclude that the new tax formula did not change the individual tax amounts significantly, which is what we wanted.

Lastly, we need to make the new plan is revenue neutral, meaning the total amount is roughly the same as before. We add back the 3 values of the unimproved properties that we removed before, and find the sum of the total tax collected before and after the new proposed tax plan. The previous sum of all tax collected is $86,666.60. The sum of taxes collected under the new plan will be $86,774.92. As the totals are very close in number, we see that the new tax plan is revenue neutral as we wanted, so we are able to propose the new plan using the formula we found.

Bibi prose form;

Ryder Appraisal District Case

Name of group members

Department

MBAD 6224 –Data Analysis and Decision Making

Dr. Murat Tarimcilar

November 14, 2021

Executive Summary

Introduction

When performing a t-test, our null hypothesis is that the actual square footage of the properties is statistically equivalent to the measurements already recorded in the database. Our alternative hypothesis is that there is a significant different between the measures. If we reject the null hypothesis, it means that all houses will have to be re-measured. When performing the t-test, we get a P value of .65. means that we do not reject the null and we do not need to re-measure all houses, and we can just use the recorded square footage already in the database. Now, to figure out what the new tax system should be, we are going to use the recorded square footage data to come to a conclusion.

In the case, the dependent variable is tax while the independent variable is the recorded square footage. The formula is given by;

Tax paid = slope * recorded square footage + y intercept

Before figuring this out, we have to keep in mind that the data given to us gives the taxes paid per property with the discounts factored in. The 10% reduction if the owner lives in the house, and the 10% reduction if the owner is retired must be removed from the data in order to figure out the correct tax rate formula. In addition, when doing the analysis, we removed the 3 data points of the unimproved properties

Results

Conclusion