(b) Find the equation of the least-squares line. (Round your values to four decimal places.)\(\hat{y} = \underline{\hspace{2cm}} + \left(\underline{\hspace{2cm}}\right)x\)(c) Use the least-squares line to predict survival rate for a community with a mean call-to-shock time of 8 minutes. (Round your answer to three decimal places.)\(\underline{\hspace{2cm}}\) **Study on Cardiac Arrest and Defibrillator Shock Timing**Studies indicate that individuals who experience sudden cardiac arrest have improved survival chances if a defibrillator shock is rapidly administered. The question explored here is: How is the survival rate influenced by the duration between the occurrence of cardiac arrest and the administration of the defibrillator shock?The data provided examines the relationship between the survival rate (y, in percent) and the mean call-to-shock time (x, in minutes) for both a cardiac rehabilitation center (where arrests occur while victims are hospitalized, leading to shorter call-to-shock times) and four different communities of varying sizes.**Data Table:**| **Mean call-to-shock time, x (minutes)** | 2 | 6 | 7 | 9 | 12 ||------------------------------------------|----|----|----|----|----|| **Survival rate, y (percent)** | 91 | 46 | 32 | 6 | 4 |**Explanation:**- The table illustrates that as the mean call-to-shock time increases, the survival rate significantly decreases. For instance, with a call-to-shock time of 2 minutes, the survival rate is 91%, but it drops to 4% with a 12-minute delay.- This data highlights the critical importance of minimizing the time between cardiac arrest occurrence and defibrillator intervention to improve survival outcomes.

Given data, X Y X*Y X*X 2 91 182 4 6 46 276 36 7 32 224 49 9 6 54 81 12 4 48 144

Answered: Find the equation of the least-squares…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Paragraph Styles 1. Police investigators and forensic scientists can often predict the height of a suspect just from a footprint that was left behind at a crime scene. This is because the size of a person's foot tends to relate to the height of a person. As you might already know, this is a positive relationship. The taller the person, the larger their feet tends to be. Data given below: Length of footprint (cm) Height (cm) a) Determine the least squares regression line 29.8 29.3 27.5 31.1 32.6 22.5 176.1 179.4 172.2 184.2 179.0 157.3 b) Determine the linear correlation coefficient c) Create a scatter plot to display the data and draw the line of best fit.
In baseball, two statistics, the ERA (Earned Run Average) and the WHIP (Walks and Hits per Inning Pitched), are used to measure the quality of pitchers. For both measures, smaller values indicate higher quality. The following computer output gives the results from predicting ERA by using WHIP in a least-squares regression for the 2017 baseball season. Variable DF Estimate SE T Intercept 1 -5.0 0.26 - 19.3 WHIP 1 6.8 0.14 47.4 Which of the following statements is the best interpretation of the value 6.8 shown in the output? ERA is predicted to increase by 6.8 units for each 1 unit increase of WHIP. WHIP is predicted to increase by 6.8 units for each 1 unit increase of ERA. For a pitcher with 0 units of WHIP, the ERA is predicted to be approximately 6.8 units. For a pitcher with 0 units of ERA, the WHIP is predicted to be approximately 6.8 units. Approximately 6.8% of the variability in ERA is due to its linear relationship with WHIP.
Draw a graph of the least-squares regression line on your scatterplot. (For hand-drawing, round the slope and y-intercept to one decimal place before drawing the line.) Be sure to show how you were able to plot the line starting with its equation. Model City Miles per Gallon Highway Miles per Gallon Acura RLX 20 29 BMW 530i 24 34 Buick LaCrosse eAssist 25 35 Chevrolet Malibu 29 36 Ford Hybrid FWD 43 41 Honda Civic 32 42 Infiniti Q50 Red Sport 20 26 Kia Forte 30 40 Lexus ES 350 22 33 Mercedes Benz AMG S 21 30 Mini Cooper Clubman 24 32 Nissan Maxima 20 30 Suburu Legacy AWD 25 34 Toyota Prius ECO 58 53
Find the equation of the least-squares line for the given data. Draw a scatter diagram for the given data and graph the least-squares line. x 1, 3, 5, 7, 9 y 9, 7, 6, 3 ,2
Considering the values of r and r2, does it make sense to use the least-squares line for prediction? Explain your answer.
determine whether the statement is true or false. If the statement is false, rewrite it as a true statement. The y-intercept b0 of a least-squares regression line has a useful interpretation only if the x-values are either all positive or all negative.
This table shows the average heights for American boys in 1990. Age (years) Height (cm) birth 50.8 2 83.8 3 91.4 5 106.6 7 119.3 10 137.1 14 157.5 Decide which variable should be the independent variable and which should be the dependent variable. Draw a scatter plot of the data. Does it appear from inspection that there is a relationship between the variables? Why or why not? Calculate the least-squares line. Put the equation in the form of: ŷ = a + bx Find the correlation coefficient. Is it significant? Find the estimated average height for a one-year-old. Find the estimated average height for an eleven-year-old. Does it appear that a line is the best way to fit the data? Why or why not? Are there any outliers in the data? Use the least squares line to estimate the average height for a sixty-two-year-old man. Do you think that youranswer is reasonable? Why or why not? 10. What is the slope of the least-squares (best-fit) line?…
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Find the equation of the least-squares line. (Round your values to four decimal places.) Use the least-squares line to predict survival rate for a community with a mean call-to-shock time of 8