T. The data in the table below are the geographic latitudes (LATITUDE) and the average August temperature in degrees Fahrenheit (AVETEMP) for a sample of 14 cities in the United States. SPSS output for these data is given at the bottom of the page. (i) Test using a = 0.05 whether there is a decreasing linear relationship between average temperature and latitude. ii) Estimate the mean average temperature for all cities in the United States with latitude 30. (iii) Give a 95% confidence interval for your estimate in part (ii). (iv) Predict the average temperature for a city in the United States with latitude 40. [v) Give a 95% confidence interval for your prediction in part (iv). (vi) Predict the average temperature for a city in the United States with latitude 44. (vii) Give the sample correlation coefficient. (viii) What proportion of the variability in average temperature in the data may be explained by the linear regression on latitude? LATITUDE 26 30 31 33 34 35 37 38 39 40 42 43 45 46 AVETEMP 83 82 82 92 75 81 77 64 74 71 72 68 71 69 Model Summary Adjusted R Std. Error of Model R R Square Square the Estimate .7428 551 .513 5.2289 a. Predictors: (Constant), LATITUDE b. Dependent Variable: AVETEMP ANOVA b Model Sum of Squares df Mean Square F Sig Regression 402.262 402.262 14.713 .002 Residual 328.095 12 27.341 Total 730.357 13 Coefficients Standar Unstandardized dized Coefficients Coefficients Mode B Std. Error Beta Sig. (Constant) 10.645 9.195 12.033 000 LATITUDE -.940 .245 -.742 -3.836 002 latitude avetemp pre_1 Imci_1 umcl_1 lici_1 uici_1 26.00 83.00 86.19658 79.54502 92.84813 73.00422 99.38893 30.00 82.00 82.43523 77.58364 87.28683 70.05246 94.81800 31.00 82.00 81.49490 77.04651 85.94329 69.26448 93.72532 33.00 92.00 79.61423 75.87250 83.35595 67.62275 91.60570 34.00 75.00 78.67389 75.21519 82.13259 66.76769 90.58009 35.00 81.00 77.73355 74.49391 80.97319 65.88913 37.00 77.00 75.85288 72.80780 78.89796 64.06019 -87.64557 38.00 64.00 74.91255 71.82757 77.99752 63.10949 86.71560 39.00 74.00 73.97221 70.75783 77.18659 62.13467 85.80974 40.00 71.00 73.03187 69.60871 76.45503 61.13595 84.92780 42.00 72.00 71.15120 67.12610 75.17630 59.06830 83.23410 43.00 68.00 70.21087 65.81779 74.60394 58.00046 82.42127 45.00 71.00 68.33019 63.11424 73.54615 55.80018 80.86021 46.00 69.00 67.38986 61.73162 73.04810 54.66937 80.11034