Regression and Correlation Analysis
Use the dependent variable Selling Price (labeled Y) and the independent variables Age, Rooms, Baths (labeled X1, X2, and X3) in the data file. Use Excel to perform the regression and correlation analysis to answer the following.
1. Generate a scatterplot for the specified dependent variable (Y) and the one of the independent variables X1, X2, or X3 including the graph of the "best fit" line. Interpret.
2. Determine the equation of the "best fit" line, which describes the relationship between the dependent variable and the selected independent variable.
3. Determine the coefficient of correlation. Interpret.
4. Determine the coefficient of determination. Interpret.
5. Test the utility of this regression model. Interpret results, including the p-value.
6. Based on the findings in Steps 1-5, analyze the ability of the independent variable to predict the designated dependent variable.
In an attempt to improve the model, use a multiple regression model to predict the dependent variable, Y, based on all of the independent variables, X1, X2, and X3.
7. Using Excel, run the multiple regression analysis using the designated dependent and three independent variables. State the equation for this multiple regression model.
8. Perform the Global Test for Utility (F-Test). Explain the conclusion.
9. Perform the t-test on each independent variable. Explain the conclusions and clearly state how the analysis should proceed. In particular, which independent variables should be kept and which should be discarded. If any independent variables are to be discarded, re-run the multiple regression, including only the significant independent variables, and summarize results with discussion of analysis.
10. Is this multiple regression model better than the linear model generated? Explain.
Selling Price 400000 370000 382500 300000 305000 320000 321000 445000 377500 460000 265000 299000 385000 430000 214900 475000 280000 457000 210000 272500 268000 300000 477000 292000 379000 295000 499000 292000 305000 520000 308000 316000 355500 225000 270000 253000 310000 300000 295000 478000
Age 27 21 36 34 69 34 35 19 40 20 39 44 33 6 49 21 49 14 64 44 44 32 19 47 29 144 62 52 36 6 42 25 46 49 24 44 53 33 34 6
Rooms 9 8 9 8 6 7 8 9 9 10 6 7 9 8 5 7 8 11 7 6 4 9 10 8 10 6 6 7 8 11 8 7 10 6 6 6 6 8 6 8
Baths (full) 3 2 2 2 2 2 1 2 3 2 2 1 3 2 1 2 2 3 1 1 1 2 4 1 3 1 2 1 3 2 2 2 2 1 1 1 2 2 2 2