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. Analysis of Variance SOURCE DF Adj SS Regression 1 41587.3 Error 7 Total 8 51984.1 Predictor Coef SE Coef T-Value Constant 20.000 3.2213 6.21 X 7.210 1.3626 5.29 Regression Equation Y = 20.0 + 7.21 X Use the F statistic to test the significance of the relationship at a 0.05 level of significance. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = Predict the selling price (in thousands of dollars) of an apartment building with gross annual rents of $65,000. $ thousand
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.
Analysis of Variance
| SOURCE | DF | Adj SS |
|---|---|---|
| Regression | 1 | 41587.3 |
| Error | 7 | |
| Total | 8 | 51984.1 |
| Predictor | Coef | SE Coef | T-Value |
|---|---|---|---|
| Constant | 20.000 | 3.2213 | 6.21 |
| X | 7.210 | 1.3626 | 5.29 |
Regression Equation
| Y = 20.0 + 7.21 X |
Use the F statistic to test the significance of the relationship at a 0.05 level of significance.
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