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Question 6 (25 marks) John would like to buy an apartment at One Beacon Hill, Kowloon Tong, so as to reduce his travel time to work. He is trying to estimate how apartment price (Y, measured in million HK dollars) is influenced by the gross floor area (X, measured in square feet). After randomly choosing 15 records from property.hk, John conducts a simple linear regression analysis on the data. The partial Excel output is shown as below: ANOVA df SS Regression 1 18701952 Residual 13 138.6375 Total 14 2008.8338 Standard Coeicients Error Intercept -9.3201 7.0544 X 0.0278 0.0021 (a) State the estimated simple linear regression equation. MS 1870.1962 10.6644 tStat -1.3212 ??? F Significance F 175.3678 6.3550509 P-value Lower 95% Upper 95% 0.2092 -24.5604 5.9202 ??? 0.0233 0.0324 (3 marks) (b) Interpret the estimated slope of the regression equation. (2 marks) (c) Find the coefficient of correlation. Interpret the result. (5 marks) (d) Use critical value approach, test the claim that there is a positive linear relationship between the apartment price and gross oor area at the level of significance 0.01. (8 marks) (e) Predict the price for an apartment with gross floor area i) 1200 square feet, and (ii) 1800 square feet. (2 marks) (f) Given that the observed X values ranged between 1400 square feet and 2500 square feet, of the two predictions obtained for (i) and (ii) in part (e), which is more justifiable? Explain why. (2 marks) (g) Discuss the significance of the intercept coefficient and suggest a modified model.