Question

5. (8 points) A student researcher went onto zillow.com to obtain the following data, for 1057 houses in Saratoga Springs: the list Price of the house in thousands of dollars, the living Area in square feet, and the number of Bedrooms. They created a linear regression to predict the Price based on Area and Bedrooms and obtained the following summary of the linear regression: Variable Estimate SE t-stat P-value (Intercept) 29.0 6.8 4.38 0.00013 Area 0.0938 0.0031 30.2 $<10^{-16}$ Bedrooms -7.48 2.78 -2.69 0.0072 $s_e$ (s.d. of the residuals) = 50.2 (a) What would you predict is the price of a 3 bedroom, 2500 square foot house? (b) If you found that one such (3 bedroom, 2500 square foot) house sold for $291,000, would you be surprised? Briefly explain. (c) As best you can, compute a 95% confidence interval for the coefficient (slope) of Area. (d) Briefly explain why the coefficient of Bedrooms might be negative, even though you would generally expect houses with more bedrooms to be more expensive. Page 4

          5. (8 points) A student researcher went onto zillow.com to obtain the following data, for
1057 houses in Saratoga Springs: the list Price of the house in thousands of dollars, the
living Area in square feet, and the number of Bedrooms. They created a linear regression
to predict the Price based on Area and Bedrooms and obtained the following summary
of the linear regression:
Variable Estimate SE t-stat P-value
(Intercept) 29.0 6.8 4.38 0.00013
Area 0.0938 0.0031 30.2 $<10^{-16}$
Bedrooms -7.48 2.78 -2.69 0.0072
$s_e$ (s.d. of the residuals) = 50.2
(a) What would you predict is the price of a 3 bedroom, 2500 square foot house?
(b) If you found that one such (3 bedroom, 2500 square foot) house sold for $291,000,
would you be surprised? Briefly explain.
(c) As best you can, compute a 95% confidence interval for the coefficient (slope) of
Area.
(d) Briefly explain why the coefficient of Bedrooms might be negative, even though you
would generally expect houses with more bedrooms to be more expensive.
Page 4

5. (8 points) A student researcher went onto zillow.com to obtain the following data, for
1057 houses in Saratoga Springs: the list Price of the house in thousands of dollars, the
living Area in square feet, and the number of Bedrooms. They created a linear regression
to predict the Price based on Area and Bedrooms and obtained the following summary
of the linear regression:
Variable Estimate SE t-stat P-value
(Intercept) 29.0 6.8 4.38 0.00013
Area 0.0938 0.0031 30.2 <10^-16
Bedrooms -7.48 2.78 -2.69 0.0072
se (s.d. of the residuals) = 50.2
(a) What would you predict is the price of a 3 bedroom, 2500 square foot house?
(b) If you found that one such (3 bedroom, 2500 square foot) house sold for 291,000,
would you be surprised? Briefly explain.
(c) As best you can, compute a 95% confidence interval for the coefficient (slope) of
Area.
(d) Briefly explain why the coefficient of Bedrooms might be negative, even though you
would generally expect houses with more bedrooms to be more expensive.
Page 4

Added by Gregory S.

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