A sample of 30 houses that were sold in the last year was taken. The value of the house (y) was estimated. The independent variables included in the analysis were the number of rooms (x₁), the size of the lot (x₂), the number of bathrooms (x₃), and a dummy variable (x₄), which equals 1 if the house has a garage and equals 0 if the house does not have a garage. The following results were obtained:

a.Write out the estimated equation.
b.Interpret the coefficient on the number of rooms (x₁).
c.Interpret the coefficient on the dummy variable (x₄).
d.What are the degrees of freedom for the sum of squares explained by the regression (SSR) and the sum of squares due to error (SSE)?
e.Test whether or not there is a significant relationship between the value of a house and the independent variables. Use a .05 level of significance. Be sure to state the null and alternative hypotheses.f. Test the significance of 1 at the 5% level. Be sure to state the null and alternative hypotheses.g. Compute the coefficient of determination and interpret its meaning.h. Estimate the value of a house that has 9 rooms, a lot with an area of 7,500, 2 bathrooms, and a garage.

Question

A sample of 30 houses that were sold in the last year was taken. The value of the house (y) was estimated. The independent variables included in the analysis were the number of rooms (x₁), the size of the lot (x₂), the number of bathrooms (x₃), and a dummy variable (x₄), which equals 1 if the house has a garage and equals 0 if the house does not have a garage. The following results were obtained:

a.Write out the estimated equation.
b.Interpret the coefficient on the number of rooms (x₁).
c.Interpret the coefficient on the dummy variable (x₄).
d.What are the degrees of freedom for the sum of squares explained by the regression (SSR) and the sum of squares due to error (SSE)?
e.Test whether or not there is a significant relationship between the value of a house and the independent variables. Use a .05 level of significance. Be sure to state the null and alternative hypotheses.f. Test the significance of 1 at the 5% level. Be sure to state the null and alternative hypotheses.g. Compute the coefficient of determination and interpret its meaning.h. Estimate the value of a house that has 9 rooms, a lot with an area of 7,500, 2 bathrooms, and a garage.

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The Answer of A sample of 30 houses that were sold in the last year was taken. The value of the house (y) was estimated. The independent variables included in the analysis were the number of rooms (x₁), the size of the lot (x₂), the number of bathrooms (x₃), and a dummy variable (x₄), which equals 1 if the house has a garage and equals 0 if the house does not have a garage. The following results were obtained: a.Write out the estimated equation. b.Interpret the coefficient on the number of rooms (x₁). c.Interpret the coefficient on the dummy variable (x₄). d.What are the degrees of freedom for the sum of squares explained by the regression (SSR) and the sum of squares due to error (SSE)? e.Test whether or not there is a significant relationship between the value of a house and the independent variables. Use a .05 level of significance. Be sure to state the null and alternative hypotheses.f. Test the significance of 1 at the 5% level. Be sure to state the null and alternative hypotheses.g. Compute the coefficient of determination and interpret its meaning.h. Estimate the value of a house that has 9 rooms, a lot with an area of 7,500, 2 bathrooms, and a garage.

A Sample of 30 Houses That Were Sold in the Last