FloorArea (Sq.Ft.) Offices Entrances Age AssessedValue ($'000) 4790 4 2 8 1796 4720 3 2 12 1544 5940 4 2 2 2094 5720 4 2 34 1968 3660 3 2 38 1567 5000 4 2 31 1878 2990 2 1 19 949 2610 2 1 48 910 5650 4 2 42 1774 3570 2 1 4 1187 2930 3 2 15 1113 1280 2 1 31 671 4880 3 2 42 1678 1620 1 2 35 710 1820 2 1 17 678 4530 2 2 5 1585 2570 2 1 13 842 4690 2 2 45 1539 1280 1 1 45 433 4100 3 1 27 1268 3530 2 2 41 1251 3660 2 2 33 1094 1110 1 2 50 638 2670 2 2 39 999 1100 1 1 20 653 5810 4 3 17 1914 2560 2 2 24 772 2340 3 1 5 890 3690 2 2 15 1282 3580 3 2 27 1264 3610 2 1 8 1162 3960 3 2 17 1447 Construct a multiple regression model. Use Excel’s Analysis ToolPak to conduct a regression analysis with AssessmentValue as the dependent variable and FloorArea, Offices, Entrances, and Age as independent variables. What is the overall fit r^2? What is the adjusted r^2? Which predictors are considered significant if we work with α=0.05? Which predictors can be eliminated? What is the final model if we only use FloorArea and Offices as predictors? Suppose our final model is: AssessedValue = 115.9 + 0.26 x FloorArea + 78.34 x Offices What wouldbe the assessed value of a medical office building with a floor area of 3500 sq. ft., 2 offices, that was built 15 years ago? Is this assessed value consistent with what appears in the database?
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
FloorArea (Sq.Ft.) | Offices | Entrances | Age | AssessedValue ($'000) |
4790 | 4 | 2 | 8 | 1796 |
4720 | 3 | 2 | 12 | 1544 |
5940 | 4 | 2 | 2 | 2094 |
5720 | 4 | 2 | 34 | 1968 |
3660 | 3 | 2 | 38 | 1567 |
5000 | 4 | 2 | 31 | 1878 |
2990 | 2 | 1 | 19 | 949 |
2610 | 2 | 1 | 48 | 910 |
5650 | 4 | 2 | 42 | 1774 |
3570 | 2 | 1 | 4 | 1187 |
2930 | 3 | 2 | 15 | 1113 |
1280 | 2 | 1 | 31 | 671 |
4880 | 3 | 2 | 42 | 1678 |
1620 | 1 | 2 | 35 | 710 |
1820 | 2 | 1 | 17 | 678 |
4530 | 2 | 2 | 5 | 1585 |
2570 | 2 | 1 | 13 | 842 |
4690 | 2 | 2 | 45 | 1539 |
1280 | 1 | 1 | 45 | 433 |
4100 | 3 | 1 | 27 | 1268 |
3530 | 2 | 2 | 41 | 1251 |
3660 | 2 | 2 | 33 | 1094 |
1110 | 1 | 2 | 50 | 638 |
2670 | 2 | 2 | 39 | 999 |
1100 | 1 | 1 | 20 | 653 |
5810 | 4 | 3 | 17 | 1914 |
2560 | 2 | 2 | 24 | 772 |
2340 | 3 | 1 | 5 | 890 |
3690 | 2 | 2 | 15 | 1282 |
3580 | 3 | 2 | 27 | 1264 |
3610 | 2 | 1 | 8 | 1162 |
3960 | 3 | 2 | 17 | 1447 |
Construct a multiple regression model.
- Use Excel’s Analysis ToolPak to conduct a
regression analysis with AssessmentValue as the dependent variable and FloorArea, Offices, Entrances, and Age as independent variables. What is the overall fit r^2? What is the adjusted r^2? - Which predictors are considered significant if we work with α=0.05? Which predictors can be eliminated?
- What is the final model if we only use FloorArea and Offices as predictors?
- Suppose our final model is:
- AssessedValue = 115.9 + 0.26 x FloorArea + 78.34 x Offices
- What wouldbe the assessed value of a medical office building with a floor area of 3500 sq. ft., 2 offices, that was built 15 years ago? Is this assessed value consistent with what appears in the database?
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