23. In the data set a sh measuring 38.9 cm weighed 510 grams. Calculate the residual t. for the model using this observation. 24. What proportion of the variation in weight.- is explained by the variation in lenghtr? 25. Calculate the adjusted R2 (r?) for the model. 26. What is the standard error for the regression (i.e. a") in problem 16? 27. What is the estimated weight of a sh 40.3 cm long? 28. Based on the previous problem, calculate an approximate 90% condence interval for the actual weight of the sh. 29. Consider the following estimated model: f'=78.830+ 0.957X2 70.00962 X22 R2 =0.5137 n=20 (2.198) (0117) {0.000146} You wish to nd out whether there is a non-linear relationship between X2 and Y and therefore perform a ttest on 33. What are the null and alternative hypothesis? 30. What is the value of the test statistic for the test in the previous problem? 31. What is the conclusion of the test? a. We keep the null hypothesis at all the usual levels of signicance (Le. 10%, 5% and 1%). b. We reject the null hypothesis at all the usual levels of signicance (i.e. 10%, 5% and 1%). c. We reject the null hypothesis at the 10% and 5% levels, but not at the 1% level. d. We reject the null hypothesis at the 10% level, but not at the 5% and 1% levels. 32. Consider the following estimated model: l7=i2l.255+9.301-lnX2 R2 =0.1850 n=100 (1.032} (1.972} Calculate 13' when X2 = 60. 33. Give an interpretation of the slope B: in the previous problem. Remaining Problems (16 -44) 16. As part of a study of the Bream fish, 39 specimens (n = 39) were caught. Their weight was recorded in grams and their length in cm. The following model was calculated: (This model will be used for question 16 -25) weight = b + b, . length (125.899) (3.222) where the numbers in brackets are the standard deviations of the calculated values for b, and b2 . Further calculations show: weight = 627.28 length = 38.80 Sw/ = 815.423 SW = 197.483 S,=4.656 Where s, is the sample covariance between weight and length and s,, and s, are the sample standard deviations of weight and length. Calculate the size of the slope b, and the constant bi. 17. Give an interpretation of the slope b2 . 18. Calculate a 95% confidence interval for the constant term. 19. You wish to test whether there is a positive relationship between length and weight. What are the null and alternative hypotheses for the test? 20. What is the value of the test statistic? 21. What is the p-value for the test? 22. The conclusion of the test is: a. We keep the null hypothesis at all the usual levels of significance (i.e. 10%, 5% and 1%). b. We reject the null hypothesis at all the usual levels of significance (i.e. 10%, 5% and 1%). c. We reject the null hypothesis at the 10% and 5% levels, but not at the 1% level. d. We reject the null hypothesis at the 10% level, but not at the 5% and 1% levels.Overnalrlngar 34. 35. 36. 37. A new model was calculated from the same data set as in problem 29: =70.6752+0.8365-1nX R2 =0.2098 (0.589) (0.154) n=100 Calculate I; when X = 60. Hint: f' z e\" Can you determine which is the better model of the two (problems 29 and 32)? If yes Which is the better model, and why? If no Explain why. Give an interpretation of the slope B: in the model in problem 34. Last year more Norwegians than usual spent their holidays in Norway. Very many chose to go to Lofoten in Norland county. The gures below give an indication of how the demand for holidays in Norland have developed over time. Overnight stays in July Growth in overnight stays in Julyr 150000 200000 ' | 120000 I 00000 I 15 10 PI'OSOHK 'I 1985 I I I I I I I I I I I I I I I 1990 1995 2000 2005 2010 2015 2020 1985 1990 1995 2000 2005 2010 2015 2020 The graph on the left shows the number of overnight stays for July of each year, while the graph on the right shows the percentage grth in overnight stays from July in year t 1 to July in year t. The growth in 2020 was a record 17.4525%. Let gnightSr be the percentage growth from year t l to year I. To estimate the growth for July 2021 the following AR(1) model was calculated (the numbers in brackets are the standard errors of the estimators): gmgin'sf = 01.237730641139933? gn:ght's,_1 + H: 11:33 R2 = 0.0000 6 = 7.3950 Use the AR(1) model to estimate the growth for 2021. 38. 39. 40. 41. 42. 43. 44. Based on the estimate from the previous problem, calculate a 90% condence interval for the actual growth in 2021. What is the condence interval? The following model can be used to test the AR(1) model for autocorrelation up to and including order p: ii, =51,+a2gnights,_l+cl,_l+czzi,_2 +5)I 1: =31 R2 =O.1014 What is p? What are the null and alternative hypotheses? What is the value of the test statistic? What is the conclusion of the test? The following model can be used to test the error term of the ARU) model for heteroscedasticity: iif = a1 + azgnightsH + a3gm'ghtsil + c?)' n = 33 R2 = 0.0514 What is the conclusion of the test? Yet another model was calculated (the numbers in brackets are the standard errors of the estimators): gags, = 3.0500 n = 34 R2 = 0.0000 (1.2481) Use the model to make a new estimate for the growth in 2021. Based on the AR(1) model: Use backward elimination as selection method with 5% as signicance level. What is the end model