(a) Predict the price of a 10 year old house which has $1000 taxes, 3 bathrooms,
ID: 3309286 • Letter: #
Question
(a) Predict the price of a 10 year old house which has $1000 taxes, 3 bathrooms, a 10000 sq. foot lot, 2000 sq. feet of living space, 2 garage stalls, 8 rooms, 4 bedrooms, and 1 fireplace. (Can use r)
(b) Use the computer output (no calculations are needed) to statistically test whether the coefficients of taxes and of number of baths are really nonzero. Provide a clear statement concerning the evidence that supports your argument, and write down a clear conclusion.
(c) Why might somebody legitimately dispute the conclusion you reached in the previous question?
1. Consider the data which relate the sale price y of a home to a number of other variables in the table.b4 data frame in the MPV package. This data frame contains the following columns: x1 taxes (in thousands of dollars) x3 lot size (in thousands of square feet) x9 no. of fireplaces x4 living space (in thousands of sq. feet) x5 no. of garage stalls x6 no. of rooms x2 number of baths x7 no. of bedrooms x8 age of the home (in years) Stepwise regression using AIC was conducted as follows. (y ~ ., data = table . b4) b4.1mExplanation / Answer
By using AIC the regression model is as
y = 13.51 + 2.42x1 + 8.48x2 + 2x5 - 2.18x7
a) we take only values $1000 taxes, 3 bathrooms, 2 garage stalls and 4 bedrooms. Then y predict is as
y = 13.51 + 2.42*1000 + 8.48*3 + 2*2 - 2.18*4
=13.51 + 2420 + 25.44 + 4 - 8.72
= 2454.23
Price is $2454.23
b)
Let , p-value for the coefficient of the taxes is less than 0.05, therefore we reject null hypothesis , i.e. Coefficients of taxes are not really nonzero.
And p-value for the coefficient of the number of baths is also less than the 0.05 , therefore we reject null hypothesis , i.e. Coefficients of number of baths are not really nonzero.
c) We say in previous que. Coefficients of taxes and number of baths are sometime zero. But it is not possible, Because every where their is taxes on houses and each house include minimum 1 bath must.
So, somebody legitimately dispute the conclusion of previous question.
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