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# Regression Analysis and Hypothesis Test

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The Director of a Real Estate Economics consulting firm is hired to determine better ways property values. However, the clients do not have background in statistics. In order to analyze the data (and get their questions answered), they have hired you as a statistical consultant to answer these questions:

Run a complete model using all variables in the data set where: Y(selling price in \$000) = a+b1X1 (number of bedrooms)+ b2X2 (size of the home in square feet)+ b3X3 (pool; 1= yes, 0 = no)+ b4X4 (distance from center of city in miles)+ b5X5 (township)+ b6X6 (Garage attached; 1 = yes, 0 = no)+ b7X7 (number of bathrooms)

a. Determine which independent variable has the strongest correlation with selling price.

b. Comment on multicollinearity

c. Conduct a test of hypothesis to determine if any of the regression coefficients are not equal to zero.

d. Determine which of the regression coefficients is not equal to zero.

e. Would you consider deleting any of the independent variables?

VARIABLES

X1 = Selling price in \$000

X2 = Number of bedrooms

X3 = Size of the house in square feet

X4 = Pool (1 = yes, 0 = no)

X5 = Distance from center of the city in miles.

X6 = Township

X7 = Garage Attached (1 = yes, 0 = no)

X8 = Number of bathrooms

Number of observations (n) = 105

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#### Solution Summary

The solution provides step-by-step method of performing a Regression Analysis and a Regression Hypothesis Test in EXCEL. All the steps of hypothesis testing (formulation of null and alternate hypotheses, selection of significance level, choosing the appropriate test-statistic, decision rule, calculation of test-statistic and conclusion) have been explained and the Regression Analysis has been shown in details.

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