## Analyzing a Data Set Using Scatter Diagrams and RegressionA data set is given below, consisting of the variables $ x $ and $ y $:\[\begin{array}{c|cccccc}x & 1 & 1 & 4 & 4 & 6 & 6 \\\hliney & 5.1 & 6.5 & 4.9 & 3.9 & 2.4 & 2.8 \\\end{array}\]### Tasks:**(a) Draw a Scatter Diagram**Select the correct graph that represents the scatter plot of the provided data set. The options are labeled A, B, C, and D.- **Progression of Points:** Review the placement of the data points on each graph to identify patterns in the relationship between $ x $ and $ y $.**Determine Relationship:**Identify if the relationship appears to be linear, quadratic, or another form from the visual analysis. The options for the relationship type will usually include terms like "positive linear," "negative linear,” or "non-linear."**(b) Calculate Least-Squares Regression Line**Given data: $ \bar{x} = 3.8667, \, s_x = 2.2509, \, \bar{y} = 4.2667, \, s_y = 1.5397, \, r = -0.9156 $.Calculate the line of best fit using the least-squares regression formula:\[y' = \text{(slope)} \times x + \text{(intercept)}\]Round the slope and intercept to three decimal places.**(c) Graph the Least-Squares Regression Line**Choose the correct graph that depicts the scatter plot with the regression line superimposed. The options are labeled A, B, C, and D:- **Line Representation:** Ensure the line accurately reflects the calculated regression equation and visually fits the data points.By following these steps, you can effectively represent the relationship between $ x $ and $ y $ using scatter diagrams and regression analysis. This process helps identify trends and make predictions based on the data.

a) Use the excel to draw the scatter plot of the given data points: The correct option for the…

A data set is given below. (a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y. (b) Given that x= 3.6667, s, =2.2509, y = 4.2667, s, = 1.5397, and r= -0.9156, determine the least-squares regression line. (c) Graph the least-squares regression line on the scatter diagram drawn in part (a). 1 4 4 5.1 6.5 4.9 3.9 2.4 2.8 (a) Choose the correct graph below. O A. OB. Oc. OD. 7- There appears to be relationship. (b) ý =x+O (Round to three decimal places as needed.) (c) Choose the correct graph below. O A. OB. OC. OD.

A data set is given below. (a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y. (b) Given that x= 3.6667, s, =2.2509, y = 4.2667, s, = 1.5397, and r= -0.9156, determine the least-squares regression line. (c) Graph the least-squares regression line on the scatter diagram drawn in part (a). 1 4 4 5.1 6.5 4.9 3.9 2.4 2.8 (a) Choose the correct graph below. O A. OB. Oc. OD. 7- There appears to be relationship. (b) ý =x+O (Round to three decimal places as needed.) (c) Choose the correct graph below. O A. OB. OC. OD.

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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Is It Getting Harder to Win a Hot Dog Eating Contest?Every Fourth of July, Nathan’s Famous in New York City holds a hot dog eating contest. The table below shows the winning number of hot dogs and buns eaten every year from 2002 to 2015, and the data are also available in HotDogs. The figure below shows the scatterplot with the regression line. Year Hot Dogs 2015 62 2014 61 2013 69 2012 68 2011 62 2010 54 2009 68 2008 59 2007 66 2006 54 2005 49 2004 54 2003 45 2002 50 Winning number of hot dogs in the hot dog eating contest Winning number of hot dogs and buns Click here for the dataset associated with this question. (a) Is the trend in the data mostly positive or negative? Positive Negative (b) Using the figure provided, is the residual larger in 2007 or 2008?Choose the answer from the menu in accordance to item (b) of the question statement 20072008 Is the residual positive or…
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Report the equation of the regression line and interpret it in the context of the problem
A data set is given below. (a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y. (b) Given that x = 3.6667, sx =2.4221, y = 3.8667, sy = 1.8435, andr= -0.9525, determine the least-squares regression line. (c) Graph the least-squares regression line on the scatter diagram drawn in part (a). D O A. (a) Choose the correct graph below. Ay 6- X y 0 0 2 3 5 6 6 5.8 5.7 5.0 2.8 1.7 2.2 O G B. Ay 6- Q (...) C. 0- ● Q D. Ау 0- X 6
(e) Find the least-squares regression line treating square footage as the explanatory variable.
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st e this 1:33 38% K A pediatrician wants to determine the relation that exists between a child's height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences, and obtains the accompanying data. Complete parts (a) through (g) below. Click the icon to view the children's data. (a) Find the least-squares regression line treating height as the explanatory variable and head circumference as the response variable. Data Table y = X + (Round the slope to three decimal places and round the constant to one decimal place as needed.) View an example Height (inches), X Head Circumference (inches), y D 27.75 17.8 24.75 17.3 25.75 17.4 26.25 17.7 25 17.1 28.25 17.9 26.75 17.5 27 17.7 26 26 27.5 ||| = Print Get more help. (...) 17.5 17.7 17.8 1 LTE2 + ... Done O X Clear all Check answer