Can you help me understand how to do a linear regression case. I don't really understand linear regression. I really want to understand how to do it. But I don't how I can share the case with you. I need step by step help, if that's possible.

Here is the problem:

Ryder Appraisal District

Ryder Appraisal District (RAD) is the county agency responsible for property taxation in Ryder County, South Carolina.RAD is charged with the appraisal of property for tax purposes, the determination of the amount of tax owed by a property owner, and the collection of these property taxes.There are approximately 12,000 residential properties in Ryder County.

James Bradford was elected last year to the position of Ryder County Tax Commissioner. For many years, taxpayers have complained about the inequities in residential property tax assessments in Ryder County. Bradford promised county residents that, if elected, he would do what he could to make the property taxing system more equitable.

The current residential property taxing system in Ryder County has evolved over several decades.Unimproved property, i.e., a residential lot without a house, is currently taxed at a flat amount of $150.Owners of improved residential property are charged a flat amount plus an additional amount based on the characteristics of the house built on the property, such as the total square footage of heated/cooled floor space, the number of bedrooms, the number of bathrooms, etc.If the owner actually lives in the house, he is given a homestead exemption which reduces his property tax bill by a fixed 10%.If that homeowner is also retired, he is entitled to a retirement exemption that reduces his property tax bill by an.ther 10%.While it would seem that the current system of taxing is fair, several factors have led to inequities.

Each year, new property assessments are mailed out to property owners. These assessments tell the property owners the value of their property as determined by RAD for taxing purposes. After the new assessments are mailed, the property owners are given the opportunity over a period of one month to contest their assessments. A panel known as the County Review Board hears the appeals and makes any adjustments they deem necessary to property assessments.The County Review Board has been known in the past for being "too responsive" in changing assessed values. Those homeowners who complain to the Board are usually granted their reduction. Unfortunately, many of these decisions have led to taxing inconsistencies and discrepancies across the county.

RAD is supposed to reappraise each piece of residential property once every three yeas. In this way, the RAD data base is kept up to date and includes recent improvements to residential property, such as swimming pools or other additions.However, due to poor economic conditions, county governments have been receiving less and less funding from the state and federal governments. The appraisal staff at RAD has dwindled in the past few years to one full-time appraiser and there are no funds available for hiring professional appraisers on a part-time basis.Over time, the data base has become outdated and inaccurate. This, of course, has led to further inequities in the taxing system.

James Bradford has proposed a simplified property tax assessment plan that he hopes will avoid the problems and inequities of the past ad cost less to implement than the current system.His plan is to tax unimproved property in the same way as before using the current rate based on lot size.For improved properties, the new tax will consist of a flat tax plus an amount based on the square footage of heated/cooled space in the house.Both the flat tax and the variable tax components are yet to be determined. Bradford has decided to maintain the current 10% reductions for homestead exemptions and retired homeowners. The square footage measurement would be made once for each house, with an appraisal update occurring whenever an addition is made to the house.This will reduce the workload of RAD appraisers and the amount of necessary recordkeeping.The simplified taxing system should also result in more consistency in taxation and fewer complaints from homeowners about incorrect assessments.

There have been two major concerns expressed about switching to the simplified tax assessment plan.First, it is important to try to keep individual taxes under the new plan as close as possible to what they are currently, otherwise there will be problems. Everyone understands that some property owners will have higher taxes and others will have lower taxes, but the size of the changes should be minimized as much as possible.Secondly, the new tax plan must be revenue-neutral, that is, the total amount of property taxes under the new structure should be roughly the same as before.James Bradford has said that attention to the first concern will largely mitigate this second concern.

The current database contains information on the square footage each house in Ryder County. Bradford believes that these data may not be accurate.In most cases, the recorded square footage is reported by the builder and is never checked by RAD.Before launching a massive effort to determine the square footage of each house in Ryder County, Bradford has decided to see whether or not the current data are sufficiently accurate.

In fact, James Bradford believes that he can kill two birds with one stone. He has collected a random sample of 80 residential properties from around the county. Over the course of the past two moths, the staff appraiser has examined the houses on these properties and their blueprints to come up with an accurate estimate of the actual square footage heated/cooled space of each house.Other information from the RAD data base was also included in the sample information.From this sample, James Bradford wants to do two things.First, he wants to know whether or not the square footage estimates in the current data base differ significantly from the actual square footage values.Secondly, he wants to use the sample to estimate the flat tax and the tax rate per square foot that must be charged in order to minimize the changes from the current tax system for improved property owners.

Assignment

The data from the sample of 80 residential properties are contained in the file RYDER.JMP on Blackboard, Session 12. The Data Description section contains a description of this data file.

Using this data set and other information given in the case, first help James Bradford decide whether or not the square footage information in the data base is significantly different from the actual values.After that, determine the flat tax amount and the tax charged per square foot that will accomplish his goals. Use important details from your analysis to support your recommendation.