hw4_soln4 - Homeworks 10-12 - Solutions 3.18 (a) To obtain...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Homeworks 10-12 - Solutions 3.18 (a) To obtain the least squares regression equation, first we will compute the slope and the vertical intercept using the equations provided in Section 3.3. ( 29 ( 29 ( 29 ( 29 62615 . 14 517 652289939 . 14 346 : Also 652289939 . 93 . 002 , 20 71 . 047 , 13 , 93 . 002 , 20 14 517 095 , 39 71 . 047 , 13 14 346 517 825 , 25 2 = - = - = = = = = - = = - = x b y a S S b So S S xx xy xx xy Thus, the equation for the least squares line is: x y 6523 . 0 626 . 0 ˆ + = (b) ( 29 46 . 23 35 65228939 . 62615 . ˆ , 35 When = + = = y x The corresponding residual is: ( 29 ( 29 46 . 2 46 . 23 21 ˆ - = - = - = y y residual 3.21 (c) The least squares line is y ˆ = 3.2925 + .10748x. For a beam whose modulus of elasticity is x = 40, the predicted strength would be y ˆ = 3.2925 + .10748(40) = 7.59. The value x = 100 is far beyond the range of the x values in the data, so it would be dangerous (i.e., potentially misleading) to extrapolate the linear relationship that far. (d) From the printout, SSResid = 18.736, SSTo = 71.605, and the coefficient of determination is r 2 = .738 (or, 73.8%) . The r 2 value is large, which suggests that the linear relationship is a useful approximation to the true relationship between these two variables.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
3.22 Using Minitab to run this regression, we obtain the following least squares regression line: x y 00882 . 0 86 . 2 ˆ + = The anova function in R gives: SS Exp = 0.2273, SS Resid = 0.00911. 3.23 (a) From the 'Parameter Estimate' column of the printout, the least squares line is y ˆ = 3.620906 - 0.014711x, where x = fracture strength. Substituting the value x = 50 into the equation gives a predicted attenuation of y ˆ = 3.620906 - 0.014711(50) = 2.8854, or, about 2.89. (b) From the 'Sum of Squares' column of the printout, SSResid = .26246 and SSTo = 2.55714. The r 2 value is .8974, or 89.74%. s ε is called the 'Root MSE' (where MSE stands for 'mean square error') in the printout, so s ε = .14789. The high vale of r 2 and the small value of s ε (compared to the typical size of the y data values) indicate
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 9

hw4_soln4 - Homeworks 10-12 - Solutions 3.18 (a) To obtain...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online