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Chapter 12: Q. 10 (page 761)

Ideal proportions The students in Mr. Shenk's class measured the arm spans and heights (in inches) of a random sample of 18 students from their large high school. Some computer output from a least-squares regression analysis on these data is shown below. Construct and interpret a 90% confidence interval for the slope of the population regression line. Assume that the conditions for performing inference are met.

Short Answer

Expert verified

We are 90% confident that the slope of the true regression line is between 0.69915114 and 0.98168886.

Step by step solution

01

Given Information

Given:

n=18

SEb=0.08091

02

Explanation

The degrees of freedom is the sample size decreased by 2 :

df=n-2=18-2=16

The critical t-value can be found in table B in the row of d f=16 and in the column of c=90% :

t*=1.746

The boundaries of the confidence interval then become:

localid="1650689704858" b-t*脳SEb=0.84042-1.746脳0.08091=0.69915114

localid="1650689713665" b+t*脳SEb=0.84042+1.746脳0.08091=0.98168886

We are 90% confident that the slope of the true regression line is between 0.69915114 and 0.98168886.

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Most popular questions from this chapter

Foresters are interested in predicting the amount of usable lumber they can harvest from various tree species. They collect data on the diameter at breast height (DBH) in inches and the yield in board feet of a random sample of 20Ponderosa pine trees that have been harvested. (Note that a board foot is defined as a piece of lumber 12inches by 12inches by 1inch.) A scatterplot of the data is shown below

(a) Some computer output and a residual plot from a least squares regression on these data appear below. Explain why a linear model may not be appropriate in this case.

(B) Use both models to predict the amount of usable lumber from a Ponderosa pine with diameter 30inches. Show your work.

(c) Which of the predictions in part (b) seems more reliable? Give appropriate evidence to support your choice.

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role="math" localid="1652870715985" PredictorCoefSE CoefTPConstant4.54590.61667.37<0.0001Dose4.83231.01644.750.0004S=3.135R-Sq=38.4%R-Sq(adj)=37.7%

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(ii) The yintercept

(iii) s

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(v) r2

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