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Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The table below shows the heights (in feet) and the number of stories of six notable buildings in a city. Height, x Stories, y 60- 800 775 53 Height (feet) 619 47 Q 519 46 OB. Find the regression equation. y=x+ (Round the slope to three decimal places as needed. Round the y-intercept to two decimal places as needed.) Choose the correct graph below. Q. A. 60 508 42 A 0 0 491 37 800 Height (feet) 474 36 D *** OC. 60- (a)x= 503 feet (c) x= 310 feet 0 800 Height (feet) .…... (b)x=642 feet (d) x = 730 feet OD. 60 800 0 Height (feet) Q

Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The table below shows the heights (in feet) and the number of stories of six notable buildings in a city. Height, x Stories, y 60- 800 775 53 Height (feet) 619 47 Q 519 46 OB. Find the regression equation. y=x+ (Round the slope to three decimal places as needed. Round the y-intercept to two decimal places as needed.) Choose the correct graph below. Q. A. 60 508 42 A 0 0 491 37 800 Height (feet) 474 36 D *** OC. 60- (a)x= 503 feet (c) x= 310 feet 0 800 Height (feet) .…... (b)x=642 feet (d) x = 730 feet OD. 60 800 0 Height (feet) Q

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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**Educational Content: Regression and Scatter Plot Analysis** **Data Analysis Task:** Given a data set representing the heights (in feet) and the number of stories of six notable buildings in a city, the goal is to find the regression line that best fits this data. **Data Table:** - **Height (x):** 775, 619, 519, 508, 491, 474 - **Stories (y):** 53, 47, 46, 42, 37, 36 **Objective:** 1. Determine the equation of the regression line for the given data. 2. Construct a scatter plot and draw the regression line. 3. Use the regression equation to predict the value of \( y \) for each specified \( x \)-value, if meaningful. **Specified \( x \)-Values for Prediction:** - (a) \( x = 503 \) feet - (b) \( x = 642 \) feet - (c) \( x = 310 \) feet - (d) \( x = 730 \) feet **Instructions:** 1. **Find the Regression Equation:** The equation of the regression line is in the form: \[ \hat{y} = b_0 + b_1x \] Calculate the slope (\( b_1 \)) and y-intercept (\( b_0 \)), rounding the slope to three decimal places and the intercept to two decimal places. 2. **Choose the Correct Scatter Plot:** Among the four provided options (A, B, C, D), choose the graph that accurately represents the data points and the regression line. **Graph Descriptions:** - **Graph A:** Features a negative slope. - **Graph B:** Features a positive slope with data points close to the line. - **Graph C:** Features a steep positive slope. - **Graph D:** Features a moderate positive slope with some variance. 3. **Predict Values:** Use the derived regression equation to predict the number of stories \( y \) for each given \( x \)-value. This exercise involves analyzing data to identify trends and make predictions using statistical methods, a foundational skill in statistics and data science.
Transcribed Image Text:**Educational Content: Regression and Scatter Plot Analysis** **Data Analysis Task:** Given a data set representing the heights (in feet) and the number of stories of six notable buildings in a city, the goal is to find the regression line that best fits this data. **Data Table:** - **Height (x):** 775, 619, 519, 508, 491, 474 - **Stories (y):** 53, 47, 46, 42, 37, 36 **Objective:** 1. Determine the equation of the regression line for the given data. 2. Construct a scatter plot and draw the regression line. 3. Use the regression equation to predict the value of \( y \) for each specified \( x \)-value, if meaningful. **Specified \( x \)-Values for Prediction:** - (a) \( x = 503 \) feet - (b) \( x = 642 \) feet - (c) \( x = 310 \) feet - (d) \( x = 730 \) feet **Instructions:** 1. **Find the Regression Equation:** The equation of the regression line is in the form: \[ \hat{y} = b_0 + b_1x \] Calculate the slope (\( b_1 \)) and y-intercept (\( b_0 \)), rounding the slope to three decimal places and the intercept to two decimal places. 2. **Choose the Correct Scatter Plot:** Among the four provided options (A, B, C, D), choose the graph that accurately represents the data points and the regression line. **Graph Descriptions:** - **Graph A:** Features a negative slope. - **Graph B:** Features a positive slope with data points close to the line. - **Graph C:** Features a steep positive slope. - **Graph D:** Features a moderate positive slope with some variance. 3. **Predict Values:** Use the derived regression equation to predict the number of stories \( y \) for each given \( x \)-value. This exercise involves analyzing data to identify trends and make predictions using statistical methods, a foundational skill in statistics and data science.
**Educational Content: Understanding Regression Lines Through Building Data** To find the equation of the regression line for the provided data, follow these instructions. You will also need to create a scatter plot of the data and draw the regression line. Note that the variable pair shows a significant correlation. Use the regression equation to predict the values of \( y \) for given \( x \)-values, if applicable. The table lists the heights (in feet) and the number of stories of six notable buildings in a city. **Data Table:** | Height, \( x \) (feet) | Stories, \( y \) | |------------------------|------------------| | 775 | 53 | | 619 | 47 | | 519 | 46 | | 508 | 42 | | 491 | 37 | | 474 | 36 | **Tasks:** 1. **Predict the value of \( y \) for \( x = 642 \):** - A. 47 - B. 31 - C. 40 - D. not meaningful 2. **Predict the value of \( y \) for \( x = 310 \):** - A. 31 - B. 47 - C. 52 - D. not meaningful *Note: The given options (a, b, c, d) for \( x \) include specific building heights such as 503 feet, 642 feet, 310 feet, and 730 feet. Calculate and choose the most appropriate number of stories for each height using the regression line equation.* Visual representations such as scatter plots and regression lines help in understanding the relationships between different variables, such as building height and the number of stories.
Transcribed Image Text:**Educational Content: Understanding Regression Lines Through Building Data** To find the equation of the regression line for the provided data, follow these instructions. You will also need to create a scatter plot of the data and draw the regression line. Note that the variable pair shows a significant correlation. Use the regression equation to predict the values of \( y \) for given \( x \)-values, if applicable. The table lists the heights (in feet) and the number of stories of six notable buildings in a city. **Data Table:** | Height, \( x \) (feet) | Stories, \( y \) | |------------------------|------------------| | 775 | 53 | | 619 | 47 | | 519 | 46 | | 508 | 42 | | 491 | 37 | | 474 | 36 | **Tasks:** 1. **Predict the value of \( y \) for \( x = 642 \):** - A. 47 - B. 31 - C. 40 - D. not meaningful 2. **Predict the value of \( y \) for \( x = 310 \):** - A. 31 - B. 47 - C. 52 - D. not meaningful *Note: The given options (a, b, c, d) for \( x \) include specific building heights such as 503 feet, 642 feet, 310 feet, and 730 feet. Calculate and choose the most appropriate number of stories for each height using the regression line equation.* Visual representations such as scatter plots and regression lines help in understanding the relationships between different variables, such as building height and the number of stories.
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775 53
619 47
519 46
508 42
491 37
474 36
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