Chapter14 - -. 780 Chapter 14 Inference f or Regression...

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- . 780 Chapter 14 Inference for Regression ACTIVITY 14 *-.- "~,, . * -- &f~~ika1a;~@&j&ijy!fiz& . -* b@cist.~B;-calGu~~t~r I diarrhited~muvius said $it '?fyou open your legs so mugh as to,decreasernr h$ight by 1/14 and spread and raise your arms til your middle fingers touch the level of the 'top ~f your head, you must know that the center of , the outspread limbs will be in tbe navel and the space between the l.e@ will be an equilateral ~igngle. . . . The leg& of a man's ~utspread~anm is eqd to hjs height" r hnwdo da Vinoi, the renowned painter, drew hla/MRe50~~e the illustration above for a book on t+e wotks of Vitruvius. Da Vinci believed that the hu~~ b.& adi!@med, t& b set gf geometric proportions as shown bp the lines isla' &rd~s. in hidrawing - B ?his a~tlvi'iy, w& want io determine if arm span can predict height. You wil~ $wd a hkic measuring tape, and you should work in teams of three: the person tp be lllieasured and two people to hold the ends of the tape. You should CQJ~~O~ at lle3@?@@2fl p?iB ofmeasurements. If your class has fewer students, recruit some volunteers from other classes. Remember: the more, the better. T&e turns taking these two m&~urements and recording them. First measure your arm span: distance between the tips of the fingers when you stretch y&ui imq~ out to he sib (the x-values). Then measure your height (the y-values). Unlike Vitruviud~ man, ivho made an equilateral tri- angle with his legs, you will keep your heels together and stand tall. Combine your results with those of the other groups. %. Make a scatterplot of the data. Clearly2 the association should be posi- - tive. 1s if? Wodd you describe the association as strong, moderate, or weak? 3. UE your calculator to perform least-squares regression and find the val- 'ue' 's,f i. and 9. Plot $he least-squares line on your scatterplot. Write a state- ment &at hjerprets the meaning, in context, of the least-squares line and vaIp,~ df r2 that you found. 4. .~&nsft~@t a fesidu;ll plot to assess whether a line is an appropriate model. for these data. Write a sentence that interprets pur residual plot. Keep your data: we will use them later in the chapter. 14.1 INFERENCE ABOUTTHE MODEL When a scatterplot shows a linear relationship between a quantitative explanatory variable x and a quantitative response variable y, we can use the least-squares line fitted to the data to predict y for a pen value of x. Now we want to do tests and confidence intervals in this setting.
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14.1 Inference about the Model 781 EXAMPLE 14.1 CRYING AND IQ Infants who cry easily may be more easily stimulated than others and this may be a sign of higher IQ. Child development researchers explored the relationship between the crying of infants four to ten days old and their later IQ test scores. A snap of a rubber band on the sole of the foot caused the infants to cry. The researchers recorded the cry- ing and measured its intensity by the number of peaks in the most active 20 seconds. They later measured the children's IQ at age three years using the Stanford-Binet I& test. Table 14.1 contains data on 38 infants. TABLE 14.1 Infants' crying and IQ scores Source: Samuel Karelitz et a]., "Relation of crying activity in early infancy to
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Chapter14 - -. 780 Chapter 14 Inference f or Regression...

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