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In this question, we investigate the relationship between the top (maximum) speed (mph) and maximum height for a random sample of roller coasters in the United States. Here is the scatterplot and a summary of the simple linear regression model.   Construct a 95% confidence interval for the true slope of the regression line and interpret your confidence interval in context.

In this question, we investigate the relationship between the top (maximum) speed (mph) and maximum height for a random sample of roller coasters in the United States. Here is the scatterplot and a summary of the simple linear regression model.   Construct a 95% confidence interval for the true slope of the regression line and interpret your confidence interval in context.

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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In this question, we investigate the relationship between the top (maximum) speed (mph) and maximum height for a random sample of roller coasters in the United States. Here is the scatterplot and a summary of the simple linear regression model.

 

Construct a 95% confidence interval for the true slope of the regression line and interpret your confidence interval in context.

### Scatterplot of Speed versus Height for Roller Coasters #### Description The scatterplot illustrates the relationship between the maximum height (in feet) and the top speed (in mph) of various roller coasters. The data points show a positive correlation, indicating that as the maximum height of a roller coaster increases, its top speed generally tends to increase as well. #### Axes - **X-axis:** Represents the maximum height of the roller coasters (in feet), ranging from 30 to 250 feet. - **Y-axis:** Represents the top speed of the roller coasters (in mph), ranging from 30 to 90 mph. #### Statistical Analysis The text below the scatterplot provides a detailed statistical analysis: - **Coefficients:** - **Intercept:** Estimate = 32.2805, Std. Error = 1.5186, t value = 21.26, p-value < 2e-16 (highly significant) - **Max_Height:** Estimate = 0.2016, Std. Error = 0.0112, t value = 18.01, p-value < 2e-16 (highly significant) - **Significance Codes:** - '***' indicates a p-value < 0.001 - '**' indicates a p-value < 0.01 - '*' indicates a p-value < 0.05 - **Residual Standard Error:** 6.029 on 109 degrees of freedom - **Multiple R-squared:** 0.7484 (indicating that approximately 74.84% of the variability in top speed can be explained by maximum height) - **Adjusted R-squared:** 0.7461 - **F-statistic:** 324.3 on 1 and 109 DF, p-value < 2.2e-16 (highly significant) This analysis suggests a strong and significant relationship between roller coaster height and speed, with a high degree of variance explained by the model.
Transcribed Image Text:### Scatterplot of Speed versus Height for Roller Coasters #### Description The scatterplot illustrates the relationship between the maximum height (in feet) and the top speed (in mph) of various roller coasters. The data points show a positive correlation, indicating that as the maximum height of a roller coaster increases, its top speed generally tends to increase as well. #### Axes - **X-axis:** Represents the maximum height of the roller coasters (in feet), ranging from 30 to 250 feet. - **Y-axis:** Represents the top speed of the roller coasters (in mph), ranging from 30 to 90 mph. #### Statistical Analysis The text below the scatterplot provides a detailed statistical analysis: - **Coefficients:** - **Intercept:** Estimate = 32.2805, Std. Error = 1.5186, t value = 21.26, p-value < 2e-16 (highly significant) - **Max_Height:** Estimate = 0.2016, Std. Error = 0.0112, t value = 18.01, p-value < 2e-16 (highly significant) - **Significance Codes:** - '***' indicates a p-value < 0.001 - '**' indicates a p-value < 0.01 - '*' indicates a p-value < 0.05 - **Residual Standard Error:** 6.029 on 109 degrees of freedom - **Multiple R-squared:** 0.7484 (indicating that approximately 74.84% of the variability in top speed can be explained by maximum height) - **Adjusted R-squared:** 0.7461 - **F-statistic:** 324.3 on 1 and 109 DF, p-value < 2.2e-16 (highly significant) This analysis suggests a strong and significant relationship between roller coaster height and speed, with a high degree of variance explained by the model.
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