INTRODUCTION TO STATITICS

Introduction to Statistics



Introduction to Statistics

Modeling Strategy

In this study we have applied the regression analysis to forecast two variables, Rent and VacRate, for the year 2011-16 periods. Both the variables are interdependent variables, it is the variable you have control over, what you can choose and manipulate. It is usually what you think will affect the dependent variable. In some cases, you may not be able to manipulate the independent variable. It may be something that is already there and is fixed, something you would like to evaluate with respect to how it affects something else, the dependent variable like colour, kind, time.

Descriptive Statistics

N

Minimum

Maximum

Mean

Std. Deviation

Rent

37

33.00

96.37

58.9854

18.97438

Output

37

19964.00

40014.00

2.9338E4

7263.41437

EmploymentFBS

37

1.68E5

3.10E5

2.4124E5

41149.23614

TakeUP

37

1648.00

6100.00

4.0127E3

1299.63578

Vacancy

37

5103.00

14702.00

1.0644E4

2538.07698

Stock

37

63161.00

95628.00

7.9431E4

11001.80023

VacRate

37

7.71

16.96

13.3251

2.32499

Valid N (listwise)

37

The table above shows the descriptive statistics for the overall data set, it gives us a clear picture. Overall there are 37 observation taken from the year 1980 - 2016, it can be said that the average rent for the mentioned time period is 58.95 £, whereas the average Vacancy rate for the time period is 13.325. The average output for the city of London is 29338 million pounds. The graphs of the data set variables suggest that the data is normally distributed and they posses the assumptions of normality.

The key variables in the data set are described below.

City Rent

Annual real rent in pounds per square feet.

City Output

Total Output of London city in million pounds.

City employment

Financial and Business Service employment

City TakeUp

Total Annual TakeUp

City Vacancy

End of year Vacancy in thousands square feet.

City Stock

End of year Total Stock.

Correlation between Rent and Vacancy

Correlations

Rent

Vacancy

Rent

Pearson Correlation

1

.025

Sig. (2-tailed)

.882

N

37

37

Vacancy

Pearson Correlation

.025

1

Sig. (2-tailed)

.882

N

37

37

The above table shows the correlation between rent and Vacancy, the results suggests that there exist a significant relationship between the two variables. Although the relationship is not too strong as the magnitude suggest there is only 25% relationship between the variables. The magnitude of significant value i.e. 0.882 suggests that the variables are not significantly different.

Multiple Regressions

Bivariate regressions are useful, but usually when we want to explain something, we have more than one independent variable that we want to control for. Let's go back to our flu example. What if we finally realize that the number of Norwegians in a zip code affects how many people there get the flu, or maybe we want to control for whether the district gave out flu shots or access to health care. In physics and engineering, when you start adding more variables, things start getting really complicated, as do the mathematics to explain them. Regressions work almost exactly the same way with 2 variables as with 3, 4, or 100. Indeed, the real payoff of regression analysis comes when we move from the bivariate case of X causing Y to the multivariate case of two or more different X's causing Y.

Model Summary

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

.781a

.610

.549

1629.04861

a. Predictors: (Constant), Stock, TakeUP, EmploymentFBS, Output

The above table represented as the model summary, describes the strength of relationship between the dependent variable and the model. The multiple correlation coefficient i.e. R represents the linear correlation between the observed and ...