ASSIGNMENT

Assignment



Assignment

Introduction

The analysis discusses the information related to gross monthly salary of a hypothetical store. The locations are changing and the information is recorded on each location. The location does not go beyond Australia. For this research, the total observations taken are 50.

Data model used

Multiple Regressions

In this analysis we are using the multiple regression models to complete our statistical analysis of the location of corner stone. The general purpose of multiple regressions (the term was first used by Pearson, 1908) is to learn more about the relationship between several independent or predictor variables and a dependent or criterion variable. For example, a real estate agent might record for each listing the size of the house (in square feet), the number of bedrooms, the average income in the respective neighborhood according to census data, and a subjective rating of appeal of the house. Once this information has been compiled for various houses it would be interesting to see whether and how these measures relate to the price for which a house is sold.

Regression Statistics

Multiple R

0.973751446

R Square

0.948191879

Adjusted R Square

0.942304593

Standard Error

14358.24005

Observations

50

The total observations being used for this analysis are 50. The Multiple R is calculated to be 0.973751446, the R square being 0.948191879. In statistics, the coefficient of determination R2 is the proportion of variability in a data set that is accounted for by a statistical model. In this definition, the term "variability" is defined as the sum of squares. There are equivalent expressions for R2 based on analysis of variance decomposition. The adjusted R square of the study is approximately 0.942304593 with a standard error being 14358.24005.

Adjusted R2 is used to compensate for the addition of variables to the model. As more independent variables are added to the regression model, unadjusted R2 will generally increase but there will never be a decrease. This will occur even when the additional variables do little to help explain the dependent variable. To compensate for this, adjusted R2 is corrected for the number of independent variables in the model. The result is an adjusted R2 than can go up or down depending on whether the addition of another variable adds or does not add to the explanatory power of the model. Adjusted R2 will always be lower than unadjusted. The term "standard error" is used to refer to the standard deviation of various sample statistics such as the mean or median. For example, the "standard error of the mean" refers to the standard deviation of the distribution of sample means taken from a population.

The smaller the standard error, the more representative the sample will be of the overall population. The standard error is also inversely proportional to the sample size; the larger the sample size, the smaller the standard error because the statistic will approach the actual value.

ANOVA Model

ANOVA

 

df

SS

MS

F

Significance F

Regression

5

1.66017E+11

33203470692

161.0575403

4.06985E-27

Residual

44

9070998522

206159057.3

Total

49

1.75088E+11

 

 

 

Functional ANOVA modeling provides a useful tool for a variety of multivariate function estimation problems. While it is more flexible than the classical linear and additive modeling, it retains the advantage of good ...