A study was conducted at Virginia Tech to determine if certain static arm-strength measures have an influence on the "dynamic lift" characteristics of an individual. Twenty-five individuals were subjected to strength tests and then were asked to perform a weightlifting test in which weight was dynamically lifted overhead. The data are given here. Individual Arm Strength, x Dynamic Lift, y 1 17.3 71.7 2 19.3 48.3 3 19.5 88.3 4 19.7 75.0 5 22.9 91.7 6 23.1 100.0 7 26.4 73.3 8 26.8 65.0 9 27.6 75.0 10 28.1 88.3 11 28.2 68.3 12 28.7 96.7 13 29.0 76.7 14 29.6 78.3 15 29.9 60.0 16 29.9 71.7 17 30.3 85.0 18 31.3 85.0 19 36.0 88.3 20 39.5 100.0 21 40.4 100.0 22 44.3 100.0 23 44.6 91.7 24 50.4 100.0 25 55.9 71.7 (a) Estimate ?? and ?? for the linear regression curve ?Y |x = ?? + ??x. (b) Find a point estimate of ?Y |30. (c) Plot the residuals versus the x's (arm strength). Comment.
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A study was conducted at Virginia Tech to determine if certain static arm-strength measures have an influence on the "dynamic lift" characteristics of an individual. Twenty-five individuals were subjected to strength tests and then were asked to perform a weightlifting test in which weight was dynamically lifted overhead. The data are given here. $$ \begin{array}{ccc} & \text { Arm } & \text { Dynamic } \\ \text { Individual } & \text { Strength, } x & \text { Lift, } y \\ \hline 1 & 17.3 & 71.7 \\ 2 & 19.3 & 48.3 \\ 3 & 19.5 & 88.3 \\ 4 & 19.7 & 75.0 \\ 5 & 22.9 & 91.7 \\ 6 & 23.1 & 100.0 \\ 7 & 26.4 & 73.3 \\ 8 & 26.8 & 65.0 \\ 9 & 27.6 & 75.0 \\ 10 & 28.1 & 88.3 \\ 11 & 28.2 & 68.3 \\ 12 & 28.7 & 96.7 \\ 13 & 29.0 & 76.7 \\ 14 & 29.6 & 78.3 \\ 15 & 29.9 & 60.0 \\ 16 & 29.9 & 71.7 \\ 17 & 30.3 & 85.0 \\ 18 & 31.3 & 85.0 \\ 19 & 36.0 & 88.3 \\ 20 & 39.5 & 100.0 \\ 21 & 40.4 & 100.0 \\ 22 & 44.3 & 100.0 \\ 23 & 44.6 & 91.7 \\ 24 & 50.4 & 100.0 \\ 25 & 55.9 & 71.7 \end{array} $$ (a) Estimate $\beta_{0}$ and $\beta_{1}$ for the linear regression curve $$ \mu_{Y \mid x}=\beta_{0}+\beta_{1} x $$ (b) Find a point estimate of $\mu_{Y \mid 30}$. (c) Plot the residuals versus the $x$ 's (arm strength). Comment.
Simple Linear Regression and Correlation
Least Squares and the Fitted Model
Weight = maximum weight capable of bench pressing (pounds) Training = number of hours spent lifting weights a week Weight = 94 + 11.6(Training) The data point is an individual who trains 5 hours a week and can bench 150 pounds. (a) Find the predicted value for the data point and compute the residual. Enter the exact answers. Predicted value= lbs Residual= lbs (b) Interpret the slope in context. Given an 11.6 hours increase in Training, expected change in Weight is 1 pound. Given a 1 pound increase in Weight, expected change in Training is 11.6 hours. Given a 1 hour increase in Training, expected change in Weight is 11.6 .
Qudsiya A.
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