A sample of 30 houses that were sold in the last year was taken.The value of the house (Y) was estimated. The independent variablesincluded in the analysis were the number of rooms (X1), the size ofthe lot (X2), the number of bathrooms (X3), and a dummy variable(X4), which equals 0 if the house does not have a garage and equals1 otherwise. The following results were obtained: CoefficientsStandard Error Intercept 15,232.5 8,462.5 X1 2,178.4 778.0 X2 7.82.2 X3 2,675.2 2,229.3 X4 1,157.8 463.1 Analysis of Variance DF SSMS Regression 204,242.88 51,060.72 Residual (Error) 205,890.008,235.60 Test whether or not there is a significantrelationship between the value of a house and the independentvariables. Use a 0.05 level of significance. Be sure to state thenull and alternative hypotheses. (f) Test thesignificance of β1 at the 5% level. Be sure to state the null andalternative hypotheses. (g) Compute the coefficient ofdetermination and interpret its meaning. (h) Estimate thevalue of a house that has 9 rooms, a lot with an area of 7,500, 2bathrooms, and 2 garages.
