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#### DescriptionThe 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 AnalysisThe 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.

The independent variable is Maximum Height. The dependent variable is Top Speed. We have to…

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

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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