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Question 4: Quadratic regression (20 points) 1. The internet movie database monitors the gross revenues for major motion pictures both in United States and internationally A student is hired to investigate the relationship between international revenue, and domestic revenue, using quadratic model. To fit the model, the values of and are collected for 19 movies The data in Millions of Dollars is shown in the table Using the excel output, please answer the questions. Movie Domestic International title (x) (y) Avatar 760.5 2021 Titanic 600.8 1234.6 The dark knight 533.3 464 E.T. 439.9 321.8 Pirates the Car ribbean 423 642.9 Jurassic park 356.8 563 Lion king 328.4 455 Harry potter 317.6 651.1 Inception 291.4 468.2 The hangover 277.3 201.6 Sixth sense 293.5 368 Jaws 260 210.6 Ghost 217.6 300 Saving private Ryan 216.1 263.2 Gladiator 187.7 268.6 Dances with wolves 184.2 240 The exorcist 204.6 153 My big fat Greek wedding 241.4 115.1 Rocky IV 127.9 172.6 SUMMARY OUTPUT Regression Statistics Multiple 0 .93330504 Square 0 87105829 Adjusted R Square 0 .85494058 Standard Error 172.95204 Observations 19 Page S of 8 ANOVA Significance df SS MS F Regression 2 3233145 1616572 54.04354 6409E 08 Residual 16 478598.5 29912.41 Total 18 3711743 Standard Upper Coefficients Error t Stat P-value Lower 95% 95% Intercept 406.423226 222.7142 1.824865 0.086749 -65.7097 878.5562 x Variable 1 -1 7929554 1.192457 1.50358 0.152171 -4. 3208512 0.73494 x2 Variable 0 00499308 0.001364 3 660346 0.002112 0.00210132 0.007885 a) Please write the least square prediction equation. (3 points) b) Find the RĀ²and interpret it. (3 points) c) Is there sufficient evidence to conclude that the overall model is useful to predict international gross revenue? (please conduct hypothesis test using alpha=0.01) (3 points) Page 6 of 8 d) Is there sufficient evidence for curvature in the model? (please conduct hypothesis test using alpha=0.05) (3 points) e) Interpret each parameter estimate (bo. b1 b2 in English words. (3 points) f) Please use the quadratic model developed to estimate the international gross revenue when domestic gross revenue is 200. (3 points) g) Please write estimate for the standard deviation of error term (2 points)

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