2) Here are the world record race times for women in the 10,000-meter run over several years. Race Time |(seconds) | 2286.4 Year a) Which is the explanatory variable and which is the response variable? | 1967 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 | 1982 e) What percent of the observed variation in the race times can be explained by your 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

2) Here are the world record race times for women in the 10,000-meter run over several years. Race Time |(seconds) | 2286.4 Year a) Which is the explanatory variable and which is the response variable? | 1967 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 | 1982 e) What percent of the observed variation in the race times can be explained by your 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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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

Answer G

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

This educational module provides historical data on the world record race times for women in the 10,000-meter run over several years. The table below presents the data:

| 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 for Analysis:

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

- The **explanatory variable** is the Year.
- The **response variable** is the Race Time (seconds).

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).**

- **Form:** The data points appear to form a linear pattern.
- **Direction:** The direction is negative, indicating that as the years increase, the race times decrease.
- **Strength:** The relationship looks strong, with points closely aligned in a descending linear trend.
- **Outliers:** There may be outliers if any data points fall far from the overall trend line.

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

To determine this, we would utilize statistical software or manual calculation of the least squares regression line. The general form is:
\[ \hat{y} = a + bx \]
where:
- $\hat{y}$ is the predicted race time.
- $a$ is the y-intercept.

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