Here are the world record race times for women in the 10,000-meter run over several years. a) Which is the explanatory variable and which is the response variable? Year Race Time (seconds) 1967 2286.4 b) Make a scatterplot of these data. You do not have to draw the scatterplot for me. Describe what you see (form, direction, 1970 2130.5 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 1982 1895.3 the race times can be explained by your 1983 1895.0 model? 1983 1887.6 f) Find the residual for the first data point or 1984 1873.8 the list (the 2286.4 seconds from 1967). 1985 1859.4 g) What does this linear model predict for th race time in the year 2075? Do you think 1986 1813.7 this is reasonable? 1993 1771.8
Here are the world record race times for women in the 10,000-meter run over several years. a) Which is the explanatory variable and which is the response variable? Year Race Time (seconds) 1967 2286.4 b) Make a scatterplot of these data. You do not have to draw the scatterplot for me. Describe what you see (form, direction, 1970 2130.5 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 1982 1895.3 the race times can be explained by your 1983 1895.0 model? 1983 1887.6 f) Find the residual for the first data point or 1984 1873.8 the list (the 2286.4 seconds from 1967). 1985 1859.4 g) What does this linear model predict for th race time in the year 2075? Do you think 1986 1813.7 this is reasonable? 1993 1771.8
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![### Historical World Record Race Times for Women's 10,000-Meter Run
#### Dataset:
| 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 Analysis:
a) **Explanatory and Response Variables:**
- The **explanatory variable** is the Year.
- The **response variable** is the Race Time (in seconds).
b) **Scatterplot Description:**
- **Form:** The scatterplot is likely to show a linear or slightly curvilinear downward trend, indicating that race times are decreasing over the years.
- **Direction:** The direction of the relationship is negative, as more recent years correlate with shorter race times.
- **Strength:** The relationship appears strong, meaning that year strongly predicts race times.
- **Outliers:** There could be outliers, but none are specified in the table.
c) **Regression Line Equation:**
- Use the least squares method to determine the regression line.
- The regression line for predicting race time from year typically has the form:
\[
\text{Race Time} = \beta_0 + \beta_1 (\text{Year})
\]
d) **Slope Meaning:**
- The slope represents the average change in race time (in seconds) for each additional year.
- **Units:** The units of the slope are seconds/year.
e) **Percentage of Variation Explained:**
- This can be found using the \( R^2 \) value from the regression analysis.
- \( R^2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F85a16b31-7619-4bbb-b006-067a19fea2d2%2Ffe86d911-d103-4652-9996-22cfda6b40b4%2Fnlpm6z.png&w=3840&q=75)
Transcribed Image Text:### Historical World Record Race Times for Women's 10,000-Meter Run
#### Dataset:
| 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 Analysis:
a) **Explanatory and Response Variables:**
- The **explanatory variable** is the Year.
- The **response variable** is the Race Time (in seconds).
b) **Scatterplot Description:**
- **Form:** The scatterplot is likely to show a linear or slightly curvilinear downward trend, indicating that race times are decreasing over the years.
- **Direction:** The direction of the relationship is negative, as more recent years correlate with shorter race times.
- **Strength:** The relationship appears strong, meaning that year strongly predicts race times.
- **Outliers:** There could be outliers, but none are specified in the table.
c) **Regression Line Equation:**
- Use the least squares method to determine the regression line.
- The regression line for predicting race time from year typically has the form:
\[
\text{Race Time} = \beta_0 + \beta_1 (\text{Year})
\]
d) **Slope Meaning:**
- The slope represents the average change in race time (in seconds) for each additional year.
- **Units:** The units of the slope are seconds/year.
e) **Percentage of Variation Explained:**
- This can be found using the \( R^2 \) value from the regression analysis.
- \( R^2
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