9 - 4/17/2011 www.lecturebook.com/homeworks/sho Assignm ent...

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Assignment Stats 250 W11 HW 9 Required Assignment Stats 250 W11 HW 9 Question 1 (Chapter 14) Correlation: Match each of the three graphs (A – C) below to one of three possible correlations: r = 0.4, r=0, r=-0.9 1. Graph A: r = 0.4, Graph B: r = 0, Graph C: r = -0.9 2. Graph A: r = 0.4, Graph B: r = -0.9, Graph C: r = 0 3. Graph A: r = 0, Graph B: r = -0.9, Graph C: r = 0.4 4. Graph A: r = 0, Graph B: r = 0.4, Graph C: r = -0.9 5. Graph A: r = -0.9, Graph B: r = 0, Graph C: r = 0.4 6. Graph A: r = -0.9, Graph B: r = 0.4, Graph C: r = 0 Solution: 6. Graph A: r = -0.9, Graph B: r = 0.4, Graph C: r = 0 Question 2 (Chapter Crawling Age for Babies. Researchers at an Infant Study Center wondered whether temperature might influence age at which babies learn to crawl. Perhaps the extra clothing that babies wear in cold weather would restrict movement and delay the age at which they started crawling. Data were collected on infant boys and girls. Parents reported the month of the baby’s birth and the age (in weeks) at which their child first crawled. The table below gives the average Temperature (°F) when the babies were 6 months old and the average Crawling Age (in weeks) for each month of the year. A scatterplot and a regression analysis were completed with SPSS and shown below. Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 6- Average 4/17/2011 www.lecturebook.com/homeworks/sho… lecturebook.com/homeworks/show/49 1/9
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a. Provide the value to complete the sentence: Based on the analysis above, about ________% of the variation in the average crawling age can be explained by the linear relationship it has with 6-month temperature. Your Answer: 61.8 Solution: 61.8 (this question is asking for the value of r 2 ) b. Give the value of the correlation between average crawling age and 6-month temperature. Your Answer: -0.786 Solution: r = -0.786 c. Give the least square regression line for estimating the average crawling age from the 6-month temperature. Your Answer: =(bo)+(b1)x Average crawling age = 36.133 + -0.085(6-month temperature) Solution: = 36.133 - 0.085(x) or in words, predicted crawling age = 36.133 – 0.085(temp) d. For babies born in August, the average temperature when they were 6 months old (so in February) was 30°F. For such babies in the sample, the average crawling age was 32.82 weeks. Find the corresponding residual for this observation. Show all work and include your units. Your Answer: Average crawling age = 36.133 + -.085(6-month temperature) x=30 =36.133 + -.085*30 = 33.583 Model R R Square Adjusted R Square Std. Error of the Estimate 1 .786 .618 .579 1.14181 ANOVA Model Sum of Squares df Mean Square F Sig. 1 Regression 21.059 1 21.059 16.153 .002 Residual 13.057 10 1.304 Total 34.096 11 Coefficients Model Unstandardized Coefficients Standardized Coefficients tS i g . B Std. Error Beta 1 (Constant) 36.133 1.134 31.859 .000 6-month Temp -.085 .021 -.786 -4.019 .002 Birth Month 6 Month Temp Average Crawling Age Jan 66 29.84 Feb 73 30.52 Mar 72 29.70 Apr 63 31.84 May 62 28.58 Jun 39 31.44 Jul 33 33.64 Aug 30 32.82 Sep 33 33.83 Oct 37 33.35 Nov 48 33.38 Dec 57 32.32 4/17/2011 www.lecturebook.com/homeworks/sho… lecturebook.com/homeworks/show/49
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9 - 4/17/2011 www.lecturebook.com/homeworks/sho Assignm ent...

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