PROBLEM 5 – HOUSING PRICES Situation: Real Estate One conducted a recent survey of house prices for properties located on the shores of Tawas Bay. Data on 26 recent sales, including the number of bathroom, square feet and bedrooms are below. Selling Price Baths Sq Ft Beds 160000 1.5 1776 3 170000 2 1768 3 178000 1 1219 3 182500 1 1568 2 195100 1.5 1125 3 212500 2 1196 2 245900 2 2128 3 250000 3 1280 3 255000 2 1596 3 258000 3.5 2374 4 267000 2.5 2439 3 268000 2 1470 4 275000 2 1678 4 295000 2.5 1860 3 325000 3 2056 4 325000 3.5 2776 4 328400 2 1408 4 331000 1.5 1972 3 344500 2.5 1736 3 365000 2.5 1990 4 385000 2.5 3640 4 395000 2.5 1918 4 399000 2 2108 3 430000 2 2462 4 430000 2 2615 4 454000 3.5 3700 4 Action: Use the data above and multiple regression to produce a model to predict the average sale price from other variables. Comment on the following: Regression equation PLACE THE ANSWER FOR PART a IN THIS SECTION DESCRIBING SHOWING THE REGRESSION EQUATION R, R2 and 1-R2, adjusted R2 PLACE THE ANSWER FOR PART b IN THIS SECTION PROVIDING THE VALUES OF R, R2, AND 1-R2 AND INTERPRETATION OF EACH ONE OF THESE VALUES. Standard error of estimate PLACE THE ANSWER FOR PART c IN THIS SECTION PROVIDING THE VALUE OF STANDARD ERROR OF ESTIMATE AND ITS INTEPRETATION. Report the t's for each value and the corresponding p-values PLACE THE ANSWER FOR PART d IN THIS SECTION PROVIDING THE t VALUES AND CORRESPONDING p VALUES FOR EACH OF THE INDEPENDENT VARIABLES. Overall test of hypothesis and decision PLACE THE ANSWER FOR PART e IN THIS SECTION. SHOW Ho AND Ha FOR OVERAL TEST OF HYPOTHESIS. COMPARE p-VALUE TO SIGINFICANCE LEVEL AND STATE WHETER Ho SHOULD BE REJECTED BASED ON THIS COMPARISON. BASED ON WHETHER Ho IS/IS NOT REJECTED, STATE WHETHER THE EQUATION PROVIDED IN PART a OF THE PROBLEM IS A GOOD PREDICTOR OF THE PRICE OF A HOUSE Use a .05 level of significance. Cite which variables are significant and which are not significant, based on the t values and p values for each independent variable. PLACE THE ANSWER FOR PART f IN THIS SECTION. EXPLAIN WHETHER BATHROOMS, SQUARE FEET, AND BEDROOMS ARE SIGNIFICANT COMPARING THE APPROPRIATE p VALUE TO THE PROBLEM STATEMENT SPECIFIED SIGNIFICANCE LEVEL.
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.
PROBLEM 5 – HOUSING PRICES
Situation:
Real Estate One conducted a recent survey of house prices for properties located on the shores of Tawas Bay. Data on 26 recent sales, including the number of bathroom, square feet and bedrooms are below.
|
Selling Price |
Baths |
Sq Ft |
Beds |
|
160000 |
1.5 |
1776 |
3 |
|
170000 |
2 |
1768 |
3 |
|
178000 |
1 |
1219 |
3 |
|
182500 |
1 |
1568 |
2 |
|
195100 |
1.5 |
1125 |
3 |
|
212500 |
2 |
1196 |
2 |
|
245900 |
2 |
2128 |
3 |
|
250000 |
3 |
1280 |
3 |
|
255000 |
2 |
1596 |
3 |
|
258000 |
3.5 |
2374 |
4 |
|
267000 |
2.5 |
2439 |
3 |
|
268000 |
2 |
1470 |
4 |
|
275000 |
2 |
1678 |
4 |
|
295000 |
2.5 |
1860 |
3 |
|
325000 |
3 |
2056 |
4 |
|
325000 |
3.5 |
2776 |
4 |
|
328400 |
2 |
1408 |
4 |
|
331000 |
1.5 |
1972 |
3 |
|
344500 |
2.5 |
1736 |
3 |
|
365000 |
2.5 |
1990 |
4 |
|
385000 |
2.5 |
3640 |
4 |
|
395000 |
2.5 |
1918 |
4 |
|
399000 |
2 |
2108 |
3 |
|
430000 |
2 |
2462 |
4 |
|
430000 |
2 |
2615 |
4 |
|
454000 |
3.5 |
3700 |
4 |
Action:
Use the data above and multiple regression to produce a model to predict the average sale price from other variables. Comment on the following:
- Regression equation
PLACE THE ANSWER FOR PART a IN THIS SECTION DESCRIBING SHOWING THE REGRESSION EQUATION
- R, R2 and 1-R2, adjusted R2
PLACE THE ANSWER FOR PART b IN THIS SECTION PROVIDING THE VALUES OF R, R2, AND 1-R2 AND INTERPRETATION OF EACH ONE OF THESE VALUES.
- Standard error of estimate
PLACE THE ANSWER FOR PART c IN THIS SECTION PROVIDING THE VALUE OF STANDARD ERROR OF ESTIMATE AND ITS INTEPRETATION.
- Report the t's for each value and the corresponding p-values
PLACE THE ANSWER FOR PART d IN THIS SECTION PROVIDING THE t VALUES AND CORRESPONDING p VALUES FOR EACH OF THE INDEPENDENT VARIABLES.
- Overall test of hypothesis and decision
PLACE THE ANSWER FOR PART e IN THIS SECTION. SHOW Ho AND Ha FOR OVERAL TEST OF HYPOTHESIS. COMPARE p-VALUE TO SIGINFICANCE LEVEL AND STATE WHETER Ho SHOULD BE REJECTED BASED ON THIS COMPARISON. BASED ON WHETHER Ho IS/IS NOT REJECTED, STATE WHETHER THE EQUATION PROVIDED IN PART a OF THE PROBLEM IS A GOOD PREDICTOR OF THE PRICE OF A HOUSE
- Use a .05 level of significance. Cite which variables are significant and which are not significant, based on the t values and p values for each independent variable.
PLACE THE ANSWER FOR PART f IN THIS SECTION. EXPLAIN WHETHER BATHROOMS, SQUARE FEET, AND BEDROOMS ARE SIGNIFICANT COMPARING THE APPROPRIATE p VALUE TO THE PROBLEM STATEMENT SPECIFIED SIGNIFICANCE LEVEL.
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