The arm span and foot length were both measured (in centimeters) for each of 20 students in a biology class. The computer output displays the regression analysis. Predictor Coef SE Coef t-ratio Constant -7.611 2.567 2.965 0.046 Arm span 0.186 0.035 5.377 0.000 Which of the following is the best interpretation of the standard deviation of the residuals? The typical arm span is 161 centimeters. The typical foot length is 16.1 centimeters. The typical distance between the observed and predicted arm spans is 1.61 centimeters. The typical distance between the observed and predicted foot lengths is 1.61 centimeters.
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TI-84 output from a linear model for predicting arm span (in centimeters) from height (in inches) is given in the figure. Summary statistics are also provided. $$ \begin{array}{|lrc|} \hline & \text { Mean } & \text { Standard Deviation } \\ \hline \text { Height, } x & 63.59 & 3.41 \\ \hline \text { Arm span, } y & 159.86 & 8.10 \\ \hline \end{array} $$ To do parts a through $\mathrm{c}$, assume that the association between arm span and height is linear. a. Report the regression equation, using the words height and arm span, not $x$ and $y$, employing the output given. b. Verify the slope by using the formula $b=r \frac{s_{y}}{s_{x}}$. c. Verify the $y$ -intercept using $a=\bar{y}-b \bar{x}$. d. Using the regression equation, predict the arm span (in centimeters) for someone 64 inches tall.
The heights (in cm) and arm spans (in cm) of 31 students were measured. The association between x (height) and y (arm span) is shown in the scatterplot below. The equation of the line of best fit modeling this relationship is given as: Y = 4.5x + 0.977 Mike is 175 cm tall and George is 170 cm tall. Using the model, how many centimeters longer would we expect Mike's arm span to be than George's?
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Arm length How long is your arm compared with your hand size? Put your right thumb at your left shoulder bone, stretch your hand open wide, and extend your hand down your arm. Put your thumb at the place where your little finger is, and extend down the arm again. Repeat this a third time. Now your little finger will probably have reached the back of your left hand. If the fourth hand width goes past the end of your middle finger, turn your hand sideways and count finger widths to get there. a) How many hand and finger widths is your arm? b) Suppose you repeat your measurement 10 times and average your results. What parameter would this average estimate? What is the population? c) Suppose you now collect arm lengths measured in this way from 9 friends and average these 10 measurements. What is the population now? What parameter would this average estimate? d) Do you think these 10 arm lengths are likely to be representative of the population of arm lengths in your community? In the country? Why or why not?
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