When an anthropologist finds skeletal remains, they need to figure out the height of the person. The height of a person (in cm) and the length of their metacarpal bone (in cm) were collected for 18 sets of skeletal remains. The data are in the table below.X, length of metacarpal (in cm) Y, height (in cm)50 17847 17540 16052 17639 15938 15741 16551 18049 17042 17545 17349 18544 17145 17341 16244 17342 16148 171a) State the random variables. rv X = of rv Y = of b) Make a scatterplot of X versus Y in StatCrunch or on your TI84. Which of the following is the correct graph? c) Find the equation of the best-fitting line (the least squares regression equation). Round values to 2 decimal places. Include the restricted domain. equation: = + * X restricted domain: cm <= X <= cmd) Interpret the slope from part c in the context of this problem. (Pay attention to the units)Every time we increase by we can expect to by on average.e) Interpret the Y-intercept from part c in the context of this problem. Include units.When is , we expect to be Does it make sense to interpret the Y-intercept on this problem? Why or why not? f) Should you use the regression equation to predict the height of a randomly selected set of skeletal remains that has a length of metacarpal of 51 cm? Should you use the regression equation to predict the height of a randomly selected set of skeletal remains that has a length of metacarpal of 61 cm? Looking at your answers above, predict the height for the one above that it made sense to do so. Make sure you use the stored equation and not the rounded equation from part c. Round final answer to 2 decimal places.The predicted height for a randomly selected set of skeletal remains that has a length of metacarpal of cm is g) Compute the residual for the following ordered pair in the data: (40, 160). Make sure you use the stored equation and not the rounded equation from part c. Round final answer to 2 decimal places. The residual for the set of skeletal remains with a length of metacarpal of 40 cm is Interpret what this value means in the context of this problem.The actual height of a randomly selected set of skeletal remains with a length of metacarpal of 40 cm is what was predicted.
Question
When an anthropologist finds skeletal remains, they need to figure out the height of the person. The height of a person (in cm) and the length of their metacarpal bone (in cm) were collected for 18 sets of skeletal remains. The data are in the table below.X, length of metacarpal (in cm) Y, height (in cm)50 17847 17540 16052 17639 15938 15741 16551 18049 17042 17545 17349 18544 17145 17341 16244 17342 16148 171a) State the random variables. rv X = of rv Y = of b) Make a scatterplot of X versus Y in StatCrunch or on your TI84. Which of the following is the correct graph? c) Find the equation of the best-fitting line (the least squares regression equation). Round values to 2 decimal places. Include the restricted domain. equation: = + * X restricted domain: cm <= X <= cmd) Interpret the slope from part c in the context of this problem. (Pay attention to the units)Every time we increase by we can expect to by on average.e) Interpret the Y-intercept from part c in the context of this problem. Include units.When is , we expect to be Does it make sense to interpret the Y-intercept on this problem? Why or why not? f) Should you use the regression equation to predict the height of a randomly selected set of skeletal remains that has a length of metacarpal of 51 cm? Should you use the regression equation to predict the height of a randomly selected set of skeletal remains that has a length of metacarpal of 61 cm? Looking at your answers above, predict the height for the one above that it made sense to do so. Make sure you use the stored equation and not the rounded equation from part c. Round final answer to 2 decimal places.The predicted height for a randomly selected set of skeletal remains that has a length of metacarpal of cm is g) Compute the residual for the following ordered pair in the data: (40, 160). Make sure you use the stored equation and not the rounded equation from part c. Round final answer to 2 decimal places. The residual for the set of skeletal remains with a length of metacarpal of 40 cm is Interpret what this value means in the context of this problem.The actual height of a randomly selected set of skeletal remains with a length of metacarpal of 40 cm is what was predicted.
Solution
a) The random variables are: rv X = length of metacarpal (in cm) rv Y = height of the person (in cm)
b) To make a scatterplot of X versus Y, you would need to plot each pair of X and Y values on a graph. Unfortunately, I can't provide a graph here, but you can easily do this in a program like StatCrunch or on a TI84 calculator.
c) To find the equation of the best-fitting line, you would need to use a method like least squares regression. This involves finding the line that minimizes the sum of the squared residuals (the differences between the observed and predicted values). Again, this can be done in a program like StatCrunch or on a TI84 calculator. The equation will be in the form Y = a + bX, where a is the Y-intercept and b is the slope. The restricted domain would be the range of X values in your data, which appears to be from 38 cm to 52 cm.
d) The slope from part c represents the expected change in Y (height) for a one-unit increase in X (length of metacarpal). So if the slope is positive, we can expect height to increase as length of metacarpal increases, and if the slope is negative, we can expect height to decrease as length of metacarpal increases.
e) The Y-intercept from part c represents the expected height when the length of metacarpal is zero. However, it may not make sense to interpret the Y-intercept in this context, because a length of metacarpal of zero is not realistic.
f) You should use the regression equation to predict the height of a randomly selected set of skeletal remains that has a length of metacarpal within the range of your data (38 cm to 52 cm). So it would make sense to predict the height for a length of metacarpal of 51 cm, but not for a length of metacarpal of 61 cm, which is outside the range of your data.
g) To compute the residual for the ordered pair (40, 160), you would need to subtract the predicted height (based on the regression equation) from the observed height. The residual represents the difference between the observed and predicted values, so a positive residual means the actual height was higher than predicted, and a negative residual means the actual height was lower than predicted.
Similar Questions
When an anthropologist finds skeletal remains, they need to figure out the height of the person. The height of a person (in cm) and the length of their metacarpal bone (in cm) were collected for 28 sets of skeletal remains. The data are in the table below.X, caloric content Y, sodium content187 499190 645111 300140 326141 386139 322177 429135 298184 482190 587176 483186 495159 374148 375132 253157 440152 330181 477131 317182 481149 319153 401149 322158 370150 326175 479176 425191 591a) State the random variables. rv X = of rv Y = of b) The symbol and value of the correlation coefficient are as follows: Round final answer to 3 decimal places.
When an anthropologist finds skeletal remains, they need to figure out the height of the person. The height of a person (in cm) and the length of their metacarpal bone (in mm) were collected for 20 sets of skeletal remains. The data are in the table below.X, length of metacarpal (in mm) Y, height (in cm)38 15742 17548 17145 17347 17546 16944 17350 18149 18547 17246 17545 17341 16542 16547 17151 18041 16240 16039 15952 176a) State the random variables. X = of Y = of b) Make a scatterplot of X versus Y in statistical software or on your computer. Which of the following is the correct graph? 38404244464850525415816016216416616817017217417617818018218438404244464850525415816016216416616817017217417617818018218438404244464850521581601621641661681701721741761781801821843840424446485052158160162164166168170172174176178180182184c) Find the equation of the best-fitting line (the least squares regression equation). Round values to 2 decimal places. Include the restricted domain. equation: = + * X restricted domain: mm <= X <= mmd) Interpret the slope from part c in the context of this problem. (Pay attention to the units)Every time we increase by we can expect to by on average.e) Interpret the Y-intercept from part c in the context of this problem. Include units.When is , we expect to be Does it make sense to interpret the Y-intercept on this problem? Why or why not? f) Should you use the regression equation to predict the height of a randomly selected set of skeletal remains that has a length of metacarpal of 44 mm? Should you use the regression equation to predict the height of a randomly selected set of skeletal remains that has a length of metacarpal of 63 mm? Looking at your answers above, predict the height for the one above that it made sense to do so. Make sure you use the stored equation and not the rounded equation from part c. Round final answer to 2 decimal places.The predicted height for a randomly selected set of skeletal remains that has a length of metacarpal of mm is g) Compute the residual for the following ordered pair in the data: (46, 169). Make sure you use the stored equation and not the rounded equation from part c. Round final answer to 2 decimal places. The residual for the set of skeletal remains with a length of metacarpal of 46 mm is Interpret what this value means in the context of this problem.The actual height of a randomly selected set of skeletal remains with a length of metacarpal of 46 mm is what was predicted.
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