4. Housing Prices in New YorkWe have looked at predicting the price (in s) of New York homes based on the size (in thousands of square feet), using the data in HomesForSaleNY. Two other variables in the dataset are the number of bedrooms and the number of bathrooms. Use technology to create a multiple regression model to predict price based on all three variables: size, number of bedrooms, and number of bathrooms. Price Size Beds Baths 145 1.3 3 1.5 875 2.9 7 3.75 300 1.5 3 2.5 370 1.1 2 1 268 1.5 2 2 1399 4.8 6 5 1125 3.1 3 2.5 299 1.4 3 2 110 1.2 3 1 2999 6 7 8 170 1 2 1 269 1.5 3 1.5 150 1 2 1.5 288 1.8 3 2.1 350 1.3 3 2 120 0.9 1 1 309 2.4 4 2.5 1500 1.5 2 1.5 635 2.5 4 2.5 350 0.9 2 1 459 1.8 4 2.5 275 2.9 4 1.5 275 1.8 3 2 2500 3.7 3 3 187 1.4 3 1.5 238 1.7 3 1.5 155 0.7 1 1 175 1.6 3 1.5 569 3.2 4 2 105 1.2 2 2.5 a) Which of the variables which are significant at the 5% level? b) Which variable is the most significant predictor in this model? c) What price does the model predict for a 1200 square foot (Size = 1.2) New York home with 3 bedrooms and 2 bathrooms? Round your answer to the nearest thousand dollars.
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.
4. Housing Prices in New York
We have looked at predicting the price (in s) of New York homes based on the size (in thousands of square feet), using the data in HomesForSaleNY. Two other variables in the dataset are the number of bedrooms and the number of bathrooms. Use technology to create a multiple regression model to predict price based on all three variables: size, number of bedrooms, and number of bathrooms.
| Price | Size | Beds | Baths |
| 145 | 1.3 | 3 | 1.5 |
| 875 | 2.9 | 7 | 3.75 |
| 300 | 1.5 | 3 | 2.5 |
| 370 | 1.1 | 2 | 1 |
| 268 | 1.5 | 2 | 2 |
| 1399 | 4.8 | 6 | 5 |
| 1125 | 3.1 | 3 | 2.5 |
| 299 | 1.4 | 3 | 2 |
| 110 | 1.2 | 3 | 1 |
| 2999 | 6 | 7 | 8 |
| 170 | 1 | 2 | 1 |
| 269 | 1.5 | 3 | 1.5 |
| 150 | 1 | 2 | 1.5 |
| 288 | 1.8 | 3 | 2.1 |
| 350 | 1.3 | 3 | 2 |
| 120 | 0.9 | 1 | 1 |
| 309 | 2.4 | 4 | 2.5 |
| 1500 | 1.5 | 2 | 1.5 |
| 635 | 2.5 | 4 | 2.5 |
| 350 | 0.9 | 2 | 1 |
| 459 | 1.8 | 4 | 2.5 |
| 275 | 2.9 | 4 | 1.5 |
| 275 | 1.8 | 3 | 2 |
| 2500 | 3.7 | 3 | 3 |
| 187 | 1.4 | 3 | 1.5 |
| 238 | 1.7 | 3 | 1.5 |
| 155 | 0.7 | 1 | 1 |
| 175 | 1.6 | 3 | 1.5 |
| 569 | 3.2 | 4 | 2 |
| 105 | 1.2 | 2 |
2.5 |
a) Which of the variables which are significant at the 5% level?
b) Which variable is the most significant predictor in this model?
c) What price does the model predict for a 1200 square foot (Size = 1.2) New York home with 3 bedrooms and 2 bathrooms? Round your answer to the nearest thousand dollars.
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