A manufacturer of boiler drums wants to use regression to predict the number of

Question

A manufacturer of boiler drums wants to use regression to predict the number of man-hours needed to erect drums in the future. The manufacturer collected a random sample of 35 boders and measured the following two variables: MANHRSyNumber of man-hours required to erect the drum RE Boiler design pressure (pounds per square inch, ie, psi The simple linear model E(v)- + 14 was fit to the data. A printout for the analysis appears below UNWEIGHTED LEAST SQUARES LINEAR REGRESSION OF MANHRS PFE DICTOR VARIABLES COEFFICIENT STD ERR( STUDENTS T P 000321 000163 2.17 04342 RESID. MEAN SQUARE (MSE) 4:25460 R-SQUARED ADIUSTED R-SQUARED 04176 STANDARD DEVIATION206267 SOURCE sS MS RESIDUA 34 144656 425160 35 255665 TOTAL Fill in the blank. Ata-.01, there is and pressure between man-hours A) sufficient evidence of a linear relationship B) sufficient evidence of a positive linear relationship C) sufficient evidence of a negative linear relationship D) insufficient evidence of a positive linear relationship In a comprehensive road test on new car models, one variable measured s the time it takes the car to accelerate from 0 to 60 miles per hour. To model acceleration time, a regression analysis is conducted on a random sample of 129 new cars. TTME60Elapsed time (in seconds) from 0 mph to 60 mph MAX Maximum speed attained (miles per hour) The simple linear model E(v)-+ n, was fit to the data. Computer printouts for the analysis are given below: NWEIGHTED LEAST SQUARES LINEAR REGRESSION OF TIMER VARIABLES COEFFICIEN ERROK NTST P 000491 17.05 MAX R-SQUARED ADIUSTED R-SQUARED 6937 STANDARD DEVIATION SOURCE 6 RESID. MEAN SQUARE (MSD2N95 13444 127 163.443 | 12M05 128 530 728 RESIDUAL TOTAL CASES INCLUDED 129 MISSING CASES Approximately what percentage of the sample variation in acceleration time can be explained by the simple linear model? A)8% B)70% C)-17% D) 0%

Explanation / Answer

1)

p-value = 0.03 > 0.01

hence variable is insignificant

option D) is correct

2) R^2 = 0.6960

hence 69.60 %   of sample variation is explained

option B) 70 % is correct

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