Three runners competed in a race. Data were collected at each mile mark for each runner. If the runner ran at a constant pace, the data would be linear. A regression line was fitted to their data. Use the residual plots to decide which data set is best fit by the regression line, and then identify the runner that kept the most consistent pace.
Question
Three runners competed in a race. Data were collected at each mile mark for each runner. If the runner ran at a constant pace, the data would be linear. A regression line was fitted to their data. Use the residual plots to decide which data set is best fit by the regression line, and then identify the runner that kept the most consistent pace.
Solution 1
To answer this question, you would need to follow these steps:
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Look at the residual plots for each runner. The residual plot shows the difference between the actual data points and the points predicted by the regression line.
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The runner whose data is best fit by the regression line will have a residual plot where the points are randomly scattered around the horizontal axis, with no clear pattern or trend. This indicates that the regression line is a good fit for the data.
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The runner who kept the most consistent pace will be the one whose data points are closest to the regression line, meaning they have the smallest residuals. This is because a smaller residual indicates that the actual data point is very close to the predicted data point, suggesting that the runner's pace was consistent.
Without the actual residual plots or data, it's impossible to identify which runner kept the most consistent pace.
Solution 2
To answer this question, you would need to follow these steps:
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Look at the residual plots for each runner. The residual plot shows the difference between the actual data points and the points predicted by the regression line.
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The runner whose data is
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If the problem involves linear velocities that are dependent on each other, we can use calculus and related rates to analyze the situation. Let's assume that the velocities of the 4 runners are represented by v1, v2, v3, and v4. If their velocities are linearly dependent, it means that there is a relationship between these velocities, such as:v1 = a1 * v2 + a2 * v3 + a3 * v4 + b1v2 = a4 * v1 + a5 * v3 + a6 * v4 + b2v3 = a7 * v1 + a8 * v2 + a9 * v4 + b3v4 = a10 * v1 + a11 * v2 + a12 * v3 + b4Here, a1 to a12 are constants, and b1, b2, b3, and b4 represent any additional external factors affecting the velocities.To solve problems involving these linearly dependent velocities, you would need to set up the system of equations and use calculus techniques, such as differentiation and optimization, to analyze the behavior of the system. This might involve finding the maximum or minimum velocity, the rate at which the velocities change, or the relationship between the velocities under various conditions.
Jacob is a marathon runner. He wants to know if a relationship exists between male runners’ ages and their marathon times. He used data from the New York City Marathon to create the scatterplot below.Select the trend line and reasoning that would best show the relationship between marathon runners' ages and race times.Group of answer choicesAn exponential trendline is best because older men tend to have much slower running times.An exponential trendline is best because men between 25 and 30 are the fastest. Race times increase for men who are both older and younger than 25–30.A quadratic trendline is best because older men tend to have much slower running times.A quadratic trendline is best because men between 25 and 30 are the fastest. Race times increase for men who are both older and younger than 25–30.A linear trendline is best because it is the simplest model of the relationship between running times and age.
Plot the residuals against the fitted values.
When do you need to add a trendline on a plot ?Group of answer choicesTo find the error level on dataTo see if data is closely matchedTo see how close data is to a special fitTo see if data is following a correct trend
Find the regression line associated with the set of points. (Round all coefficients to four decimal places.)(5, 7), (7, 11), (11, 15), (13, 3)y(x) = −0.1786x+9.9643 Graph the data and the best-fit line. (Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.)
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