I am stuck on this problem set.

Consider the sample data on Boston house prices given by the Excel file "Boston.xlsx". The definitions of each column are given below

1. CRIM: per capita crime rate by town

2. ZN: proportion of residential land zoned for lots over 25,000 sq.ft.

3. INDUS: proportion of non-retail business acres per town

4. CHAS: Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)

5. NOX: nitric oxides concentration (parts per 10 million)

6. RM: average number of rooms per dwelling

7. AGE: proportion of owner-occupied units built prior to 1940

8. DIS: weighted distances to five Boston employment centers

9. TAX: full-value property-tax rate per $10,000

10. PTRATIO: pupil (student) - teacher ratio by town

11. VALUE: Median value of owner-occupied homes in $10,000's

You have been asked to build a model that will help you estimate/explain the value of a given property in the Boston area given all the other variables (a total of 10 variables) given in the above list.

21) What is the R-Squared of your multiple linear regression model?

a) 0.72 b) 0.56 c) 0.66 d) 0.92

22) Obtain the variance inflation factor for the variable "crim" to test the existence of multi-collinearity.

a) 10 b) 2.9 c) 1.01 d) 1.56

23) What would be your estimate of a property in the Boston region for a property with the following characteristics?

crim

zn

indus

chas

nox

rm

age

dis

tax

ptratio

0.005

12

2.1

0

0.5

6

38

2

296

15.3

a) 23.5 b) 30.35 c) 23.7 d) 22.4

At a significance level of 0.01, check if the error terms of your multiple linear regression model are normally distributed (for Q24 and 25)?

24) What is the p-value of your test?

a) 0.85 b) 0 c) 0.01 d) 0.02

25) What is your conclusion?

a) Fail to reject the null hypothesis, the residuals are normally distributed.

b) Fail to reject the null hypothesis, the residuals are not normally distributed.

c) Reject the null hypothesis, the residuals are normally distributed.

d) Reject the null hypothesis, the residuals are not normally distributed.