11) A Multiple Regression Model of \"Median Home Value\" was created based on da
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11) A Multiple Regression Model of "Median Home Value" was created based on data for the 51 United States and the District of Columbia. The following is the Correlation and part of the Regression output. The dependent variable is "Median Home Value" (MEDHOMEVAL). The other variables are the Independent variables: "Robbery rate" ( ROBBERY),'%Working outside county of residence" (WORKOUTS IDE), ROWHOUSE (%),"% with 5 or more units" (5+-UNITS),'% of Housing very Crowded" ( 1.5-PER-RM), &% Houses that use LP Gas" (LP GAS). Please answer the following questions: A) The following is a correlation matrix of all the variables in the model. Are there any pair of INDEPENDENT variables thatare "multicollinear"? MEDHOMEVAL ROBBERY WORKOUTSIDEROW HOUSE 5+ UNITS 1.5 PER RM LP GAS MEDHOMEVAL ROBBERY WORKOUT SIDE ROW_HOUSE 5+ UNI 1.5 PER RM LP GAS 0.254 235 0.377 648 0.652 0.617 043 705 725 431 0.374 0.090 004 0.057 0.041 619 0.314 0.413 658 0.509 -0.404 B) The following from the regression run is a table of the Coefficients for each independent variable and the Y-Intercept of the model along with the Standard Error for each. Calculate the"" statistic for each independent variable and do a p-value hypothesis test at 5% level of significance where the null hypothesis is "B = 0" and the Alternate hypothesis is "B > 0". (For the negative coefficients the alternate hypothesis is "B 0", One tail tests for all coefficients)-Which variables are acceptable based on the p-value test? (Note: When using the "t" table, look for the nearest degree row available) Coefficients Standard Error Variable Intercept ROBBERY WORKOUTSIDE ROW_HOUSE 167,081 5+_UNITS 1.5_PER_RM LP G 81,789.7 13,355 217.8 865 52 291.7 268,303 715,776 91,600.1 73,608 224,914.3 214.9 963.0 C) Compute the Coefficient of determination (R-Square) foreach independent variable D) How many additional variables would you be allowed to add to this equation based on the heuristic rule from the last lecture?Explanation / Answer
A) Using correlation matrix we say that there is no multicoliniarity in the independent variable .
Becuase there is correlation between two variable is not near unity (closed to one) that why
0we say that there is no multicoliniarity in this data.
C) Compute the Coefficient of determination
Coefficient of determination is the square of correlation coeficient .
B) Calculate Test Statistics
To=(B1-B0)/SE(B1)
Bo=intercept
B1=slope of first variable .
SE(B1)=sandared error of B1
In this table last column is P-value is less than 0.05 those variable are significant.
D)
4 variable are Add to the final model
ROW_HOUSE
ST_UNITS
L.S_PER_RM
LP_GAS
This variable are add in the model.
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Best of Luck :)
Dependent variable ibdependent variable correlation R-square MEDHOMEVAL ROBBERY 0.254 0.064516 MEDHOMEVAL WORKOUTSIDE 0.235 0.055225 MEDHOMEVAL ROW_HOUSE 0.377 0.149904 MEDHOMEVAL ST_HOUSE 0.648 0.419904 MEDHOMEVAL L.S_PER_RM 0.652 0.425104 MEDHOMEVAL LP_GAS 0.617 0.380689Related Questions
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