Question

PART I. Multiple Choice. Cirele the letter to the correct answer on the front page 1. Below is a list of assumptions necessary for the regression analysis to be valid. With each assumption is a proposed procedure (on the right) for checking the validity of the assumption. Select the assumption validity which is the correct match. a. Normal errors b. Constant error variance C. Plot of residuals versus x Plot of residuals versus x Histogram of residuals Look for outliers Mean error equal to 0 For the following situation, (Questions 2,3,) indicate in cach case whether a correct decision has been made, or whether a Type 1 or Type II error has occurred. The null and alternative hypotheses are: HO : New system is no better than the old one HI: New system is better. 2. The old system is retained, when really the new one is better. a correct decision b) Type I error c) Type II error 3. A new system is adopted, when in fact the new one is no better a. correct decision b) Type I error c) Type II error Instruction Questions: 4,5, 6,7 Car & Driver conducts comprehensive road tests on all new car models and reports the results in the "Road Test Digest One variable measured is the time it takes a car to accelerate from 0 to 60 miles per hour. To model acceleration time, a regression analysis is conducted on the following data collected for a random sample of 129 new cars TIME60: Y - Elapsed time (in seconds) from 0 mph to 60 mph MAX: X = Maximum speed attained (miles per hour) Initially, the simple linear model E y)-β + , x was fit to the data. Computer printouts for the analysis are given below PREDICTOR VARIABLES COEFFICIENT STD ERROR STUDENT'S T CONSTANT 18.7171 -0.08365 0.63708 0.00491 29.38 0.0000 0.0000 R-SQUARED ADJUSTED R-SQUARED 0.6937 STANDARD DEVIATION 0.6960 RESID. MEAN SQUARE (MSE) 1.28695 1.13444 SOURCE MS 374.285 290.83 0.0000 1.28695 374.285 163.443 537.728 REGRESSION RESIDUAL TOTAL 1 128 CASES INCLUDED 129 MISSING CASES。 4, Fill in the blank. "At α 05, there is ween maximum speed and acceleration time." A. sufficient evidence of a negative linear relationship B I nsufficient evidence of a negative linear relationship C. sufficient evidence of a positive linear relationship D. sufficient evidence of a downward curvilinear relationship 5. Approximately what percentage of the sample variation in acceleration time the simple linear model can explain? Complete the sentence: "About 95% of the sampled new cars have acceleration times that 6. C. fall outside 1.28 miles per hour of their true values D. fall within 2.26 seconds of their predicted values A. fall within 1.13 seconds of their predicted values B. equal.696 second Practically interpret this interval. Each answer begins with We are 07 7 A 95% confidence interval for 95% confident that." 09 i is A. acceleration time will decrease between 07 and.09 second B. for every 1-second increase in acceleration time, maximum speed will decrease between 07 and.09 mile per hour. C. for a new car with a maximum speed of I mile per hour, acceleration time will fall between 07 and.09 second. D. for every 1 mile per hour increase in maximum speed, acceleration time will decrease between 07 and.09 second.

Answer 1

(1) right choice : b.

The errorshave constant variance, with the residuals scattered randomly around zero

(2) right choice: Type II error

Type II error : Accepting H0 when it false

(3) right choice : Type I error

Type I errro : Rejectin H0 when it is true

(4) right choice: C.

since p-value is less than alpha so we reject H0 of correlation is zero

(5) right choice : A

here R-sq=.6960 means 69.6 % variantion explained by independent variable in dependent variable

(6)right choice :  D.

here standard deviation(SD) is 1.13 so 95% sampled value lies in the range of $\pm$ 2SD

(7) right choice : D