Housing Data Set Boston - 1 year CRIM per capita crime rate by town ZN proportio

Question

Housing Data Set Boston - 1 year CRIM per capita crime rate by town ZN proportion of residential land zoned for lots over 25,000 sq. ft. INDUS proportion of non-retail business acres per town CHAS Charles River dummy variable (= 1 if tract bounds river; 0 otherwise) NOX nitric oxides concentration (parts per 10 million) RM average number of rooms per dwelling AGE proportion of owner-occupied units built prior to 1940 DIS weighted distances to five Boston employment centres RAD index of accessibility to radial highways TAX full-value property-tax rate per $10,000 PTRATIO pupil-teacher ratio by town B 100(Bk - 0.63) ^2 where Bk is the proportion of blacks by town LSTAT % lower status of the population MEDV Median value of owner-occupied homes in $1000’s From the variable given: Build a model to test, i.e. choose the dependent variable and the independent variable or variables. You must justify your choice of dependent variable and independent variable or variables (this means justifying excluding variables as well.) Justify whether you would expect the independent variable(s) to have a positive or negative effect on the dependent variable. You must justify your choice of a linear or non-linear model. Carefully and completely explain your results. Test - conduct all hypothesis tests discussed in class on your model.

Step 1: Establish a null and an alternative hypothesis

Step 2: Determine the appropriate statistical test

Step 3: Set the value of alpha, the Type I error rate

Step 4: Establish the decision rule

Step 5: Gather sample data

Step 6: Analyze the data

Step 7: Reach a statistical conclusion

Step 8: Make a business decision

Explanation / Answer

Our model is: CRIM = +B1ZN + B2INDUS + B3DIS + B4RAD + B5PTRATIO + B6LSTAT + B7MEDV +ui

We choose a linear model because according to our belief there are no factors which might have an exponential effect on the per capita crime rates by town.

The dependent variable is: CRIM-per capita crime rates by town. We choose CRIM(per capita crime rates by town) to be our dependent variable because the amount of crime that happens in a town may be dependent on a whole lot of other factors and may not be independent on its own (of the other variables mentioned in the question).

The independent variables that we include in our model are:

ZN-proportion of residential land zoned for over 25000sq ft. This might affect the crime rates as the more sparsely the residential area is populated the less likely it becomes to commit a crime and in more densely populated areas the competition for resources is more. So the coefficient B1 for this variable will have a positive value i.e higher the proportion of residential area allotted higher the crime rates.

INDUS- proportion of non-retail business acres per town. This might affect the crime rates because the more business are located in the town the more number of incidences might arise where a criminal act may be committed. Referring to thefts, robbery etc. So the coefficient B2 will have a positive value more the proportion of non-retail business more the crime rates.

DIS- weighted distances to five Boston employment centres. This might affect the crime rates as the father away are the employment centres the more likely it will be that the people in the town are unemployed. Unemployment means that they will be struggling for survival and have a higher chance of entering into criminal activities. So, the coefficient B3 will be positive and will have a positive effect on the crime rates. More the distance more the crime rates.

RAD- index of accessibility to radical highways. The more accessible the highways are the more easy it is to flee. Also, it might increase the exposure of the town to criminal activities. So, the coefficient B4 will have a positive effect on crime rates.

PTRATIO- the lower the pupil teacher ratio in the town the more likely it is that the town will not be properly educated. This means that their tendency to enter into criminal activities might be more due to lack of proper education and lack of other venue to earn a living. So, B5 will also have a positive effect on the crime rates.

LSTAT- proportion of lower status people in town. The higher the proportion of lower status people in town the more likely it becomes for a crime to be committed. This is because it is assumed that the people with a lower status are poor, less educated and lack basic means. So competition among them is more. So, the coefficient B6 will have a positive effect in the crime rates i.e higher the percentage of people with lower status higher the crime rates.

MEDV-medin value of owner occupied homes in town. If the value of the owner occupied homes in the town is high this means that the town is wealthy. So instances of thefts and robbery might be more.

The variables which we do not include in our model are:

CHAS-Charles river dummy variable. The proximity to the river does not effect the crime rates in any manner. So, it is not included in our model

NOX-nitric oxide concentration in parts per million. The concentration of nitric oxide does not affect the crime rates. Its an environmental factor whereas crime rates are a social factor. There is no reason to believe that one induces the other.

RM- average number of rooms per dwelling. The number of rooms per dwelling will not affect the crime rates in the town. Any effect that might be there due to overcrowding might be tapped by the variable ZN(proportion of residential land zoned for 25000sq ft).

AGE-proportion of owner occupied units built prior to 1940. This will not have any effect onn the crime rates. The age of the buildngs does not determine how crimes are committed. Any sort of relation might be spurious here

TAX- full value property tax rate per 10000. The tax rate will not affect the crime rates in the town. There is no reason to believe property value tax affect crime rates.

B- proportion of blacks in town. We are not taking race into account. In general there is no reason to believe that one particular community is involved in criminal activities. So, this variable is not included in the model.

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