The correlation matrix is given by: bath 7. (35ptn) Using the Ames Housing dataset one can use a hedonic pricing method to analyse housing prices. This a technique to determine the value of houses based on the sum of underlying values of the different characteristics of the house. The method uses linear regression based on observed house characteristics (size, construction year, number of bedrooms, etc.) to create a price estimate Based on 2000 observations and the following 4 variables: . price: sales price of the house; floor: floor space in square meters; bath: number of bathrooms, age: a dummy-variable equal to 1 if the house was built after 1975, and elsewhere; I investigated if one can ask a significantly higher price for houses built after 1975. I estimated the following regression with output: price floor age price 1.0000000 0.8153875 0.2807205 0.5558368 floor 0.8153875 1.0000000 0.2685143 0.2677710 bath 0.2807205 0.2685143 1.0000000 0.1571669 age 0.5558368 0.2677710 0.1571669 1.0000000 and the first 5 observations are given by: price Home1 181000 Home 2 124000 Home 3 72000 Home4 137000 Home 5 124500 5 floor bath ago 926 0 1 1 1584 0 0 0 0 819 0 0 o 561 1 1 864 0 0 log(price), = Bo + B floor; + Babathi + Byage; + Ei 2 7.1 (2ptn) Calculate the missing Std. Error of the variable floor. 7.2 (2ptn) Interpret the effect of the variabele age 7.3 (3ptn) Construct a confidence interval for the variabele bath and illustrate with a figure. 7.4 (2ptn) Could we have issues with quasi-multicollineary in this regression? 7.5 (4ptn) Could we have an omitted variable bias? Explain the omitted variable bias and possible solutions. 7.6 (2ptn) What does the R2 of the model mean. Provide the formula and interpreta- tion. . 7.7 (2ptn) Create a prediction for Home4 (the fourth observation) based on the model and ce. 7.8 (3ptn) How are the p-values calculated? Explain in words the meaning of the P-values. 7.9 (2ptn) What is the reduced model for the model test and how should this be interpreted? 7.10 (2ptn) What is the formula for the OLS estimator? 7.11 (5ptn) The mean of the residuals is not given as this is equal to zero by definition. Show that that is indeed the case in this regression and explain on which assumption this is based Residuals: Min 10 Median 30 Max -2.204 -0.144 0.0123 0.152 1.085 Coefficients: Estimate Std. Error t value . (Intercept) 11.270 0.019 593. 158 floor 0.284 [XXXX) 28.400 bath 0.063 0.012 5.250 age 0.377 0.012 31.417 Pr>It!) It!) It!) It!)