Question

The peanut crop was harvested from five fields of various area. The following data are the mass of the crop from each field y (in kilograms) and the field area x (in hectares).

Reserve Problems Chapter 11 Section 2 Problem 2 The peanut crop was harvested from five fields of various area. The following data are the mass of the crop from each field y (in kilograms) and the field area X (in hectares). y 7410 15590 13670 19770 13000 2.21 3.77 3.55 4.22 2.45 Round your intermediate answers to four decimal places (e.g. 98.7654). (a) Fit the simple linear regression model using the method of least squares. Find the estimate of o. Round your answer to the nearest integer (e.g. 9876). (b) What change in the mean mass is expected when the field area changes by 1 hectare? Round your answer to the nearest integer (e.g. 9876). B. = (c) Calculate the fitted value of y corresponding to x = 2.45. Find the corresponding residual. Round your answer to the nearest integer (e.g. 9876). = Round your answer to the nearest integer (e.g. 9876). e = (d) Estimate the mean mass of the crop harvested from 3.0 hectares. Rour your answer to the nearest integer (e.g. 9876). I

Answer 1

n= 5 myr ý = Syn = 69440 513 888 ma= m = 1 {\; = 16 5 = 3.24 옷 Sau Ep.mm = 3.0224 Say Say = 2(yi-my) = 80 295280 {(i-my) (x Mx) = 13972.7 2- SSE = Syy = 15698818 Sun a) SSE =5232939,5=52329 40 n-2 b) Sny san - 4623 The B = Mgr B M x = -1091 regression equation is = -1091 +46232 to a=2.45 is The fitted value corresponding û = -109174623x2.45 = 10235 Residual (2)=4-ý = 13000-10235 = 2765 s of the harvested crop from 3.0 hectares d) The meani n=3 9 = - 1891 +46 2 34 3=12778