COURSE WORK ABOUT FORECASTING USING MINITAB PROGRAM

Course work about forecasting using Minitab program

Course work about forecasting using Minitab program

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 model-predicted values of the dependent variable. Its magnitude suggests that there is a strong and positive relationship.

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.

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

-8784.861

4610.480

-1.905

.068

Output

-.261

.206

-.707

-1.264

.217

EmploymentFBS

-.009

.025

-.150

-.357

.724

TakeUP

-.222

.338

-.117

-.658

.516

Stock

.379

.081

1.479

4.686

.000

a. Dependent Variable: Vacancy

Table above represent the Coefficient table which we have extracted from the regression analysis, the equation for the vacancy variable is given below. The t statistic is the coefficient divided by its standard error. The standard error is an estimate of the standard deviation of the coefficient, the amount it varies across cases. It can be thought of as a measure of the precision with which the regression coefficient is measured. If a coefficient is large compared to its standard error, then it is probably different from 0.

Vacancy = -8784.861 - 0.261(Output) - 0.009(EmploymentFBS) - 0.222(TakeUp) + 0.379(Stock)

The forecasted values for the variable of vacancy are as follow:

Year

Vacancy

2011

14029.0

2012

13564.0

2013

13052.0

2014

13274.0

2015

13362.0

2016

13143.0

In the year 2011, it can be said that the vacancies for the employees will be comparatively higher than ...