Question

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) = b₀ + b₁x was fit to the data. Computer printouts for the analysis are given below:

PREDICTOR

VARIABLES   COEFFICIENT   STD ERROR   STUDENT'S T      P

---------   -----------   ---------   -----------   ------

CONSTANT       18.7171      0.63708      29.38      0.0000

MAX           -0.08365      0.00491     -17.05      0.0000

R-SQUARED           0.6960    RESID. MEAN SQUARE (MSE)   1.28695

ADJUSTED R-SQUARED 0.6937    STANDARD DEVIATION         1.13444

SOURCE       DF      SS          MS        F       P

---------- --- ---------- ---------- ----- ------

REGRESSION    1    374.285     374.285 290.83 0.0000

RESIDUAL    127    163.443     1.28695

TOTAL       128    537.728

CASES INCLUDED 129   MISSING CASES 0

1. Fill in the blank: "At a =.05, there is ________________ between maximum speed and acceleration time."

A.     sufficient evidence of a positive linear relationship

B.      insufficient evidence of a negative linear relationship

C.      sufficient evidence of a negative linear relationship

D.      sufficient evidence of a downward curvilinear relationship

Answer 1

As r square is 0.6960 that is coefficient of determination.

Hence r is correlation coefficient is 0.8345

So that correction coefficient equal to 0.8345 indicate that there is high positive correlation between the  X = Maximum speed attained (miles per hour) and Y= Elapsed time (in seconds) from 0 mph to 60 mph.

Hence, there is sufficient evidence of a positive linear relationship Between maximum speed and acceleration time.

Correct option is

a.sufficient evidence of a positive linear relationship.

answered by: anonymous