**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 meaningful2. **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.

Given data is x y 775 53 619 47 519 46 508 42 491 37 474 36

Answered: Find the equation of the regression…

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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The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. x 11.4 8 6.8 3.4 2.4 2.2 2.4 0.4 y 13.5 10.7 10.1 6.9 5.9 5.6 6.3 4.2 x = thousands of automatic weapons y = murders per 100,000 residents This data can be modeled by the equation y = 0.85x + 3.97. Use this equation to answer the following; Special Note: I suggest you verify this equation by performing linear regression on your calculator. A) How many murders per 100,000 residents can be expected in a state with 10.3 thousand automatic weapons? Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 4.3 thousand automatic weapons? Answer= Answer = Round to 3 decimal places.
You generate a scatter plot using Excel. You then have Excel plot the trend line and report the equation and the rí value. The regression equation is reported as y = - 38.57x + 35.79 and the r2 = 0.4096. What is the correlation coefficient for this data set? r =
Use the given data set to answer parts (a) and (b). a. Find the regression equation for the data points. b. Graph the regression equation and the data points. a. Find the regression equation for the data points. G (Use integers or decimals for any numbers in the expression. Round to two decimal places as needed.) X 5 y - 1 4 1 1 -1 3 2 2 4 Q
The table shows the approximate chirping rate at various temperatures for one type of cricket. Use the linear regression feature on a graphing calculator to determine an equation of the line that best fits the data. Round to the hundredths. ⒸEncikAn/Shutterstock.com X Temperature (°F) 50 60 70 80 100 Chirps per Minute 20 80 115 150 250
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A researcher wishes to estimate, with 99% confidence, the population proportion of motor vehicle fatalities that were caused by alcohol-impaired driving. His estimate must be accurate within 5% of the population proportion. (a) No preliminary estimate is available. Find the minimum sample size needed. (b) Find the minimum sample size needed, using a prior study that found that 36% of motor vehicle fatalities that were caused by alcohol-impaired driving. (c) Compare the results from parts (a) and (b). (a) What is the minimum sample size needed assuming that no prior information is available? n=(Round up to the nearest whole number as needed.) (b) What is the minimum sample size needed using a prior study that found that 36% of motor vehicle fatalities that were caused by alcohol-impaired driving? n=(Round up to the nearest whole number as needed.) (c) How do the results from (a) and (b) compare? OA. Having an estimate of the population proportion has no effect on the minimum sample size…
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We run the following regression using a sample of 148 women living in the western states. The variable wage is the hourly wage ( in USD) and educ is the number of years of education completed. wage = -3.07 + 1.52 educ Which statement best described the estimated slope coefficient? Group of answer choices A 1.52 extra years of education is predicted to increase wage by 1 USD An extra year of education is predicted to increase hourly wage by 1.52 USD A 1 percent increase in education is predicted to increase wage by 1.52 percent A 1.52 percent increase in education is predicted to increase wage by 1
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x	y
775	53
619	47
519	46
508	42
491	37
474	36