# Regression Analysis

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Statistics

19th December 2015

Regression Analysis

Introduction

Linear Regression is a statistical inference, from where the cause and effect relationship between two variables are assessed. It helps to predict the magnitude of one variable from the magnitude of another variable. The former variable is called criterion and the later variable is called criterion. In this article the price of real estate was estimated from the wise year prices.

Methodology

Sales data was considered from the hyperlink: https://netfiles.umn.edu/users/nacht001/www/nachtsheim/Kutner/Appendix%20C%20Data%20Sets/APPENC11.txt

Data was randomly selected and aligned to R software package. The dependent variable (criterion) was real estate price (price) while the independent variable was assessment year (year).

Hypothesis Testing

Null hypothesis contends that there is no significant relation between the two variables and one variable cannot be extrapolated to find out the value of other variable (p>0.05). On the other hand, the alternate hypothesis contends that there is significant relation between the two variables and one variable can be extrapolated to find out the value of other variable (p<0.05). Further, the relationship between the two variables may be positive or negative. This means the value of one variable may increase the value of another variable (positive correlation) or increasing the value of one variable may decrease the value of another variable (negative correlation).

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Results

Linear Regression – Estimated Regression Equation

price = +14.27032967033 year +131.04395604396

Multiple Linear Regression – Ordinary Least SquaresVariable Parameter S.E. T-STATH0: parameter = 0 2-tail p-value 1-tail p-value

ye[t] 14.27033 0.762756 18.708915 0 0

Constant 131.043956 6.49463 20.177279 0 0

Variable Partial Correlation

ye[t] 0.983287

Constant 0.98558

Critical Values (alpha = 5%)

1-tail CV at 5% 1.79

2-tail CV at 5% 2.18

R 0.983287

R-squared 0.966853

Adjusted R-squared 0.964091

F-TEST 350.023515

Observations 14

Degrees of Freedom 12

Linear Regression – Analysis of Variance

ANOVA DF Sum of Squares Mean Square

Regression 1 46328.625275 46328.625275

Residual 12 1588.303297 132.358608

Total 13 47916.928571 3685.9175824176

F-TEST 350.023515

p-value 0

Discussion & Conclusion

The above results clearly indicates that indeed real estate price and assessment year is positively correlated (p<0.05) and the regression equation is significant too (p<0.05). So, assessment year may successfully predict the price of real estate. The equation is quite robust as the R value (coefficient of determination) is nearly 97%. Moreover, the trend is linear with very few outliers.

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