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A high school track & field coach wanted to asses the relationship between an athletes height and how far they can jump in the long jump event (both in inches). They collect data on each athletes height and how far they can jump. Let the height of the athlete be the explanatory variable (X) and the length of the jump be the response (Y). The scatterplot of the data is as follows: Scatter Plot distance 88- 86 - 84 - 82 - 80 78 - 72 74 76 78 height A. Based on the scatterplot, is there a positive or negative association between height of athlete and length of jump? B. Based on the scatterplot, state why using a linear regression equation is justified to asses the relationship between height and length of jump.

A high school track & field coach wanted to asses the relationship between an athletes height and how far they can jump in the long jump event (both in inches). They collect data on each athletes height and how far they can jump. Let the height of the athlete be the explanatory variable (X) and the length of the jump be the response (Y). The scatterplot of the data is as follows: Scatter Plot distance 88- 86 - 84 - 82 - 80 78 - 72 74 76 78 height A. Based on the scatterplot, is there a positive or negative association between height of athlete and length of jump? B. Based on the scatterplot, state why using a linear regression equation is justified to asses the relationship between height and length of jump.

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
Problem 1P
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A high school track & field coach wanted to assess the relationship between an athlete's height and how far they can jump in the long jump event (both in inches). They collected data on each athlete's height and how far they can jump. Let the height of the athlete be the explanatory variable (X) and the length of the jump be the response (Y). The scatterplot of the data is as follows: **Scatter Plot Explanation:** - **X-axis (horizontal):** Represents the height of the athlete in inches. - **Y-axis (vertical):** Represents the distance of the jump in inches. - The plotted points indicate the relationship between each athlete's height and their jump distance. **Questions:** **A.** Based on the scatterplot, is there a positive or negative association between the height of the athlete and the length of the jump? **B.** Based on the scatterplot, state why using a linear regression equation is justified to assess the relationship between height and length of jump.
Transcribed Image Text:A high school track & field coach wanted to assess the relationship between an athlete's height and how far they can jump in the long jump event (both in inches). They collected data on each athlete's height and how far they can jump. Let the height of the athlete be the explanatory variable (X) and the length of the jump be the response (Y). The scatterplot of the data is as follows: **Scatter Plot Explanation:** - **X-axis (horizontal):** Represents the height of the athlete in inches. - **Y-axis (vertical):** Represents the distance of the jump in inches. - The plotted points indicate the relationship between each athlete's height and their jump distance. **Questions:** **A.** Based on the scatterplot, is there a positive or negative association between the height of the athlete and the length of the jump? **B.** Based on the scatterplot, state why using a linear regression equation is justified to assess the relationship between height and length of jump.
**C.** Which of the following (pick one only) could be a possible value of the correlation coefficient between distance and height? Explain in a sentence or two. Choices are: -1, -0.7, 0, 0.1, 0.7, 1. Now say a simple linear regression model is fit to the data. Fitting the simple linear regression model, the estimated regression equation is: \( \hat{y} = 6.4285 + 1.0534X \) **D.** What type of variable is the response (categorical or quantitative)? How about the explanatory variable? **E.** What is the predicted length of the jump for an athlete who is 72 inches tall? **F.** Interpret what the 1.0534 represents. **G.** Does the intercept of 6.4285 inches have any useful interpretation to the coach? **H.** Can the coach conclude the taller the athlete is will cause them to jump farther? **I.** The original units of measurement were Y=distance length in inches and X=height in inches. Now say the **response** variable is recorded in feet NOT inches (there are 12 inches in one foot). What will happen to the intercept estimate of 6.4285? Will it stay the same, increase, or decrease? Explain in a sentence or two. **J.** The original units of measurement were Y=distance length in inches and X=height in inches. Now say the **explanatory** variable is recorded in feet NOT inches (there are 12 inches in one foot). What will happen to the intercept estimate of 6.4285? Will it stay the same, increase, or decrease? Explain in a sentence or two. **K.** Continue with the situation in part J. Let \( \rho_1 \) be the correlation coefficient between distance in inches and height in inches. Let \( \rho_2 \) be the correlation coefficient between distance in inches and height in feet. Is \( \rho_1 \) equal to, less than, or greater than \( \rho_2 \)? Explain in a sentence.
Transcribed Image Text:**C.** Which of the following (pick one only) could be a possible value of the correlation coefficient between distance and height? Explain in a sentence or two. Choices are: -1, -0.7, 0, 0.1, 0.7, 1. Now say a simple linear regression model is fit to the data. Fitting the simple linear regression model, the estimated regression equation is: \( \hat{y} = 6.4285 + 1.0534X \) **D.** What type of variable is the response (categorical or quantitative)? How about the explanatory variable? **E.** What is the predicted length of the jump for an athlete who is 72 inches tall? **F.** Interpret what the 1.0534 represents. **G.** Does the intercept of 6.4285 inches have any useful interpretation to the coach? **H.** Can the coach conclude the taller the athlete is will cause them to jump farther? **I.** The original units of measurement were Y=distance length in inches and X=height in inches. Now say the **response** variable is recorded in feet NOT inches (there are 12 inches in one foot). What will happen to the intercept estimate of 6.4285? Will it stay the same, increase, or decrease? Explain in a sentence or two. **J.** The original units of measurement were Y=distance length in inches and X=height in inches. Now say the **explanatory** variable is recorded in feet NOT inches (there are 12 inches in one foot). What will happen to the intercept estimate of 6.4285? Will it stay the same, increase, or decrease? Explain in a sentence or two. **K.** Continue with the situation in part J. Let \( \rho_1 \) be the correlation coefficient between distance in inches and height in inches. Let \( \rho_2 \) be the correlation coefficient between distance in inches and height in feet. Is \( \rho_1 \) equal to, less than, or greater than \( \rho_2 \)? Explain in a sentence.
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