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2) Here are the world record race times for women in the 10,000-meter run over several years. Race Time (seconds) Year a) Which is the explanatory variable and which is the response variable? 1967 2286.4 b) Make a scatterplot of these data. You do | 2130.5 not have to draw the scatterplot for me. Describe what you see (form, direction, 1970 1975 2100.4 strength, outliers). 1975 2041.4 c) Write the equation of the regression line for predicting race time from year. 1977 1995.1 1979 1972.5 d) Give the meaning of the slope of your line in terms of race time and year. What are the units of the slope in this problem? 1981 1950.8 1981 1937.2 e) What percent of the observed variation in the race times can be explained by your 1982 1895.3 1983 1895.0 model? 1983 1887.6 f) Find the residual for the first data point on the list (the 2286.4 seconds from 1967). 1984 1873.8 1985 1859.4 g) What does this linear model predict for the race time in the year 2075? Do you think this is reasonable? 1986 1813.7 1993 1771.8

2) Here are the world record race times for women in the 10,000-meter run over several years. Race Time (seconds) Year a) Which is the explanatory variable and which is the response variable? 1967 2286.4 b) Make a scatterplot of these data. You do | 2130.5 not have to draw the scatterplot for me. Describe what you see (form, direction, 1970 1975 2100.4 strength, outliers). 1975 2041.4 c) Write the equation of the regression line for predicting race time from year. 1977 1995.1 1979 1972.5 d) Give the meaning of the slope of your line in terms of race time and year. What are the units of the slope in this problem? 1981 1950.8 1981 1937.2 e) What percent of the observed variation in the race times can be explained by your 1982 1895.3 1983 1895.0 model? 1983 1887.6 f) Find the residual for the first data point on the list (the 2286.4 seconds from 1967). 1984 1873.8 1985 1859.4 g) What does this linear model predict for the race time in the year 2075? Do you think this is reasonable? 1986 1813.7 1993 1771.8

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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### World Record Race Times for Women in the 10,000-meter Run The table below shows the world record race times for women in the 10,000-meter run over several years: | Year | Race Time (seconds) | |------|----------------------| | 1967 | 2286.4 | | 1970 | 2130.5 | | 1975 | 2100.4 | | 1975 | 2041.4 | | 1977 | 1995.1 | | 1979 | 1972.5 | | 1981 | 1950.8 | | 1981 | 1937.2 | | 1982 | 1895.3 | | 1983 | 1895.0 | | 1983 | 1887.6 | | 1984 | 1873.8 | | 1985 | 1859.4 | | 1986 | 1813.7 | | 1993 | 1771.8 | **Questions and Tasks:** a) **Identify Variables:** - Which is the explanatory variable and which is the response variable? b) **Scatterplot Analysis:** - Make a scatterplot of these data. You do not have to draw the scatterplot for me. Describe what you see (form, direction, strength, outliers). c) **Regression Line:** - Write the equation of the regression line for predicting race time from year. d) **Slope Interpretation:** - Give the meaning of the slope of your line in terms of race time and year. What are the units of the slope in this problem? e) **Variation Explanation:** - What percent of the observed variation in the race times can be explained by your model? f) **Residual Calculation:** - Find the residual for the first data point on the list (the 2286.4 seconds from 1967). g) **Future Prediction:** - What does this linear model predict for the race time in the year 2075? Do you think this is reasonable? ### Detailed Explanations: - **Graphs and Diagrams:** - The data could be plotted on a scatter plot with the year on the x-axis (explanatory variable) and the race times in
Transcribed Image Text:### World Record Race Times for Women in the 10,000-meter Run The table below shows the world record race times for women in the 10,000-meter run over several years: | Year | Race Time (seconds) | |------|----------------------| | 1967 | 2286.4 | | 1970 | 2130.5 | | 1975 | 2100.4 | | 1975 | 2041.4 | | 1977 | 1995.1 | | 1979 | 1972.5 | | 1981 | 1950.8 | | 1981 | 1937.2 | | 1982 | 1895.3 | | 1983 | 1895.0 | | 1983 | 1887.6 | | 1984 | 1873.8 | | 1985 | 1859.4 | | 1986 | 1813.7 | | 1993 | 1771.8 | **Questions and Tasks:** a) **Identify Variables:** - Which is the explanatory variable and which is the response variable? b) **Scatterplot Analysis:** - Make a scatterplot of these data. You do not have to draw the scatterplot for me. Describe what you see (form, direction, strength, outliers). c) **Regression Line:** - Write the equation of the regression line for predicting race time from year. d) **Slope Interpretation:** - Give the meaning of the slope of your line in terms of race time and year. What are the units of the slope in this problem? e) **Variation Explanation:** - What percent of the observed variation in the race times can be explained by your model? f) **Residual Calculation:** - Find the residual for the first data point on the list (the 2286.4 seconds from 1967). g) **Future Prediction:** - What does this linear model predict for the race time in the year 2075? Do you think this is reasonable? ### Detailed Explanations: - **Graphs and Diagrams:** - The data could be plotted on a scatter plot with the year on the x-axis (explanatory variable) and the race times in
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