need properly explained solution of all

There are important applications in which, due to Known scientic constraints, the regression line must go through the origin he, the intercept must be zero}. In otherwords, the model should read Y :lfcaIea, i:l,2,...,n, and only a simple parameter requires estimation. The model is often called the regression through the origin model. {a} Show that the least squares estimator of the slope is in : imam i133 1121 11:1 2 2 2 {DjiShowthat 0'31 2 0' Z 1121; . 12:1 {c} show that 111 in part {a} is an unbiased estimator for 51. That is, show crap = m. Test for linearity:r of regression in Exercise 11.3 on page 393. Use a o.o5 level of signicance. Comment. The amounts of a chemical oompound yr that dissolved in 1oo grams of water at 1.ran'ous temperatures 1-: 1uturere recorded as follows: I (T) 9 {grams} {1 a s a 15 12 1o 14 so 25 21 24 4s 31 33 23 so 44 so 42 1'5 43 51 44 {a} Find the equation of the regression line to} Graph the line on a scatter diagram. {C} Estimate the amount of chemical that 1will dissolve in 10D grams of water at 5U\" C. Use an analysis-of-variance approach to test the hypothesis that , = 0 against the alternative hypothesis 3, = 0 in Exercise 11.5 on page 398 at the 11.5 0.05 level of significance. A study was made on the amount of converted sugar in a certain process at various temperatures. The data were coded and recorded as follows: Temperature, a Converted Sugar, y 1.0 8.1 1.1 7.8 1.2 8.5 1.3 9.8 1.4 9.5 1.5 8.9 1.6 8.6 1.7 10.2 1.8 9.3 1.9 9.2 2.0 10.5For the data of Exercise 12.5 on page 45!], estimate 02. 12.5 The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature 1:1, the number of days in the month 22, the average product purity 1:3, and the tons of product produced 1'4. The past year's historical data are available and are presented in the nllnwing table. 1; 2:1 1*: Is 3:: 241} 25 2:1 91 11]] 236 31 21 QB 95 290 45 2:11- 33 11[II 2H ED 25 3'? 33 31111 65 25 91 9:1 316 22 26 9-1 99 em SD 25 3"! Q"? 296 34 25 BE 96 2E? 25 2:1 33 11[II WE 2E 91 105 238 5D 25 EU 11]] 261 IE 23 89 93 [a] Fit :1 multiple linear regression nrcdel using the abmre data set. [b] Predict power consumption for a nmoth in which 1'1 = \"35F, :3 = 24 days. :3 = 90%, and 1:4 = 93 tons. \fConsider the following data from Exercise 12.13- on page 452. y (wear) 31 {oil viscosity) a}: [load] 103 1.5 351 230 15.5 310 17'? 22.0 1053 01 43.0 1201 1 13 33.0 135? 125 40.0 1 1 15 {a} Estimate 02 using multiple regression of F on x1 and r2 _ {o} Compute predicted values, a 95% condence interval for mean wear, and a 95% prediction interval for observed wear if I, = 20 and x2 = moo. 12.13 A stud}; was performed on a. type of hear ing to nd the relationship of amount of wear 1: to on 2 oil viscosity.r and 1'2 2 load. The following data were obtained. {Pi-om Response Surface Methodology, Myers, Montgomery, and AndersonCook, 2000.) y 31 '32 y 31 312 103 1.5 351 230 15.5 815 172 22.0 11153 91 43.0 1201 113 33.0 1357r 125 40.0 1115 (a) Estimate the unknown parameters of the multiple linear regression equation \f\f