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 ...