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, strength, outliers). 1970 2130.5 1975 2100.4 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 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, strength, outliers). 1970 2130.5 1975 2100.4 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 1986 1813.7 this is reasonable? 1993 1771.8

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Answer only G

### World Record Race Times for Women in the 10,000-Meter Run

Below is a table containing world record race times for the 10,000-meter run for women recorded 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 |

### Exercise Questions:

**a)** Which is the explanatory variable and which is the response variable?

- **Explanation:**
- The explanatory variable is "Year" as it explains or predicts changes.
- The response variable is "Race Time (seconds)" since it responds to changes in the explanatory variable.

**b)** Make a scatterplot of these data. You do not have to draw the scatterplot for me. Describe what you see (form, direction, strength, outliers).

- **Description:**
- **Form:** The scatterplot likely shows a linear or slightly curved downwards trend.
- **Direction:** Negative correlation, as years increase, race time decreases.
- **Strength:** Strong relationship, as the points are close to a line.
- **Outliers:** Check for any points significantly deviant from the general trend line. 1975 has two entries but they are close to each other, so no obvious outliers.

**c)** Write the equation of the regression line for predicting race time from year.

- **Regression Line Equation:**
- The form is $ Race\ Time = a + b \times (Year) $
- You will calculate the exact values of $a$ and $b$ from the data using statistical software or

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