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. Based on these data he obtained the following regression results. The regression equation is Ductility = 7.67 - 3.30 Carbon Content Predictor Coef SE Coef t P-value Constant 7.671 1.507 5.09 0.000 Carbon Content -3.296 1.097 -3.01 s = 2.36317 R-Sq = 41.0% R-Sq(adj) = 36.5% i) Find a 95% confidence interval for the slope of the regression line. (6) ii) Interpret this interval. (2) iii) Can we conclude that Carbon Content is a significant predictor of Ductility? Test using α = 0.05. (3) iv) What is the p-value for the test in part iii)? (4)

Answer 1

Here,

i) a 95% confidence interval for the slope of the regression line

ii) We are 95% confident that lies within the interval (-5.66593, -0.926074)

iii) To test the significance of Carbon content,

The value of the test statistic is t = -3.01

Under H₀, the test statistic follows a t distribution with n -2 = 15 - 2 = 13 df.

and P-value =

Since P-value < 0.05, so we reject H₀ at 5% level of significance and we can conclude that Carbon Content is a significant predictor of Ductility.