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.
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 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.
Solution
a) The random variables in this case are:
rv X = Length of the metacarpal bone rv Y = Height of the person
b) To calculate the correlation coefficient, you would need to use the formula for Pearson's correlation coefficient. However, without the actual data points, it's impossible to calculate the exact value. The formula is:
r = Σ[(xi - x̄)(yi - ȳ)] / √[(Σ(xi - x̄)²)(Σ(yi - ȳ)²)]
Where: xi and yi are the individual sample points indexed with i x̄ and ȳ are the means of the x and y variables Σ is the sum of the elements
The correlation coefficient (r) ranges from -1 to 1. A value of 1 means a perfect positive correlation, -1 means a perfect negative correlation, and 0 means no correlation. The closer the coefficient is to either -1 or 1, the stronger the correlation between the variables.
Without the actual data points, we cannot calculate the correlation coefficient.
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 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.
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.
Recall the 3-variable example from before:1. X1: Intelligence2. X2: Weight3. X3: AgeSuppose that these correlations are actually based on sample size n = 20:ˆρ = 1 0.6162 0.82670.6162 1 0.73210.8267 0.7321 1
Question 8You know that there is a strong correlation between the consumption of ice cream and body weight. The Pearson's r = 0.78. You also know that the average consumption of ice cream per week is five grams with a standard deviation of 1.5 grams. The average weight is 65 kg with a standard deviation of 15 kg. What is the formula of the regression line?1 pointŷ = 26 + 7.8x ŷ = 7.8 + 26xŷ = -502 + 0.078x ŷ = 0.078 - 502x
The following data represents the scores of two variables, x and y: x: 10, 15, 20, 25, 30 y: 20, 25, 30, 35, 40 The correlation coefficient between x and y is:a.0.7b.0.8c.0.9d.1
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