Test whether the explanatory variables collectively help to explain the log of house prices

INSTRUCTIONS TO CANDIDATES

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An economist wishes to analyze how house prices depend on certain characteristics of the house in a city in the US. To this end, she takes a random sample from house sales in the city in a particular month and collects the following information: price, the house price in thousands of dollars; bdrms, the number of bedrooms in the house; sqrf t, the size of the house in square feet. The sample size is N = 88. Based on this sample, she estimates the regression model below in R,

(a) Test whether the explanatory variables collectively help to explain the log of house prices. Be sure to explain all aspects of your test including the null and alternative hypotheses in terms of restrictions on β0, how your test statistic is calculated, the decision rule and the outcome of the test. From the conventional choices of significance levels (10%, 5%, 1%), choose the one that gives the most informative answer.

(b) Test whether the number of bedrooms has a positive impact on the house price. Be sure to explain all aspects of your test including the null and alternative hypotheses expressed in terms of restrictions on β0, how your test statistic is calculated, the decision rule and the outcome of the test. From the conventional choices of significance levels (10%, 5%, 1%), choose the one that gives the most informative answer.

(c) What is the interpretation of β0,3? Justify your answer. 

(d) The economist wishes to use the regression results to calculate the impact of an increase in sqrf t by 1 on the price for a 1000 square foot house holding all other factors equal, and asks your help. Provide the answer for her: report the figure to 4 decimal places and be sure to explain your calculation. 

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