The commercial division of a real estate firm is conducting a regression analysis of the relationship between x, annual gross rents (in thousands of dollars), and y, selling price (in thousands of dollars) for apartment buildings. Data were collected on several properties recently sold and the following computer output was obtained.
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.
The commercial division of a real estate firm is conducting a
| The regression equation is | |||
| Y = 20.0 + 7.26 X | |||
| Predictor | Coef | SE Coef | T |
| Constant | 20.000 | 3.2213 | 6.21 |
| X | 7.260 | 1.3628 | 5.29 |
| Analysis of Variance | |||
| SOURCE | DF | SS | |
| Regression | 1 | 41,587.4 | |
| Residual Error | 7 | ||
| Total | 8 | 51,984.7 |
a. How many apartment buildings were in the sample?
b. Write the estimated regression equation (to 2 decimals if necessary).
ŷ = + x
c. What is the value of sb1 (to 4 decimals)?
d. Use the F statistic to test the significance of the relationship at a .05 level of significance.
Compute the F test statistic (to 2 decimals).
What is the p-value? Use Table 1 of Appendix B.
p-value is
What is your conclusion?
e. Predict the selling price of an apartment building with gross annual rents of $60,000 (to 1 decimal).
$ thousands.
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