Question

As the carbon content in steel​ increases, its ductility tends to decrease. A researcher at a steel company measures carbon content and ductility for a sample of 15 types of steel. Use the following regression results to find the​ 95% confidence interval for the slope of the regression equation. The regression equation is

Ductility = 7.67 - 3.30 Carbon Content

Predictor Coef SE Coef T P

Constant 7.671 1.507 5.09 0.000

Carbon Content -3.296 1.097 -3.01 0.010

S = 2.36317 R-Sq = 41.0% R-Sq(adj) = 36.5%

Answer 1

-5.649065 and -0.942935

Explanation:

The degree of freedom will be given by

n - 1 where n is the sample number, given here as 15 so

`D_f=15-1=14`

Critical time, t for a 95% confidence interval from the table is

`t_(crit) = 2.145`

The 95% confidence levels will be given by

Limit=Parameter estimate ± Critical t * standard error of parameter estimate.

The standard error of parameter estimate is given as 1.097

First limit=-3.296 -( 2.145*1.097 )= -5.649065

Second limit = -3.296 + (2.145*1.097) = -0.942935