The table represents the scores medical students obtained in their first and second years.| 1st Year = X | 2nd Year = Y ||--------------|--------------|| 5 | 12 || 5 | 10 || 6 | 9 || 7 | 7 || 8 | 7 || 9 | 6 |Tasks:a) Draw a scatter plotb) Find the regression linec) Find the correlation coefficientd) Find the coefficient of determinatione) Determine the linear relationship**Explanation:** The table gives the scores of students in two consecutive years, with "X" representing the first-year scores and "Y" representing the second-year scores. The tasks aim to analyze the relationship between these scores using statistical methods such as creating a scatter plot, calculating the regression line, correlation coefficient, and the coefficient of determination to understand the linear relationship between the two sets of scores.

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Answered: The table represents the scores medical…

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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In order for applicants to work for the foreign-service department, they must take a test in the language of the country where they plan to work. The data below shows the relationship between the number of years that applicants have studied a particular language and the grades they received on the proficiency exam. Find the equation of the regression line for the given data. Number of years, x 4 4 3 6 2 7 3 Grades on test, y 61 68 75 82 73 90 58 93 72 滷 O A. =6.910x+46.261 O B. y = 46.261x+6.910 OC. v=6.910x-46.261 OD. O D. y = 46.261x -6.910 Fi St 5e Assig
The arm span and foot length were both measured (in centimeters) for each of 20 students in a biology class. The computer output displays the regression analysis. Which of the following is the best interpretation of the coefficient of determination r2? About 37% of the variation in arm span is accounted for by the linear relationship formed with the foot length. About 65% of the variation in foot length is accounted for by the linear relationship formed with the arm span. About 63% of the variation in arm span is accounted for by the linear relationship formed with the foot length. About 63% of the variation in foot length is accounted for by the linear relationship formed with the arm span.
Which of the following denotes the slope or the regression coefficient for X? A) The term a B) The term b C) The error term D) The correlation coefficient, r
I. Show complete solutions. Simple Linear Regression and Correlation: a.) Results of a study on the occurrence of sodium and chloride in surface streams in a coastal area. The following data are chloride concentration (y) in mg/liter and road-way area in the watershed (x) in %. Y 0.24 4.6 1. What is the value of the correlation coefficient? 2. What is the interpretation for this case? 3. What is the estimated chloride concentration if road way 0.3 6.4 0.45 9.8 area in the watershed is 1.30% 0.75 10.7 4. What is the equation of the prediction line? 0.57 10.6 0.75 10.9 0.4 11.7 0.8 12.5 0.6 14 0.78 14.7 0.85 15.1 0.68 18.3 0.69 19.2 1.4 23.1 1.15 27.3 1.05 27.7 1.69 32 1.62 38.4
An analyst wanted to analyze the relationship between the speed of a car (x) measured in mph and its gas mileage (y). As an experiment a car is operated at several different speeds and for each speed the gas mileage is measured. These data are shown below. Speed 25 35 45 50 60 65 70 Gas Mileage 40 39 37 33 30 27 25 What is the dependent variable? What is the independent variable?
a. Using the pairs of values for all 10 points, find the equation of the regression line. b. After removing the point with coordinates (2,3), use the pairs of values for the remaining 9 points and find the equation of the regression line. c. Compare the results from parts (a) and (b).
Consider the following table, find the value of the INTERCEPT (b) of the regression line. X Values Y Values 23 8 22 25 4 24 7 21
The following table contains ACT scores and the GPA for eight college students. Estimate the relationship between GPA (yi) and ACT (x;) using OLS regression by hand. Report the intercept and slope estimates: Student 1 2 3 4 5 6 7 8 GPA 2.8 3.4 3.0 3.5 3.6 3.0 2.7 3.7 ŷ₁ =B₁ + B₁x₁ ACT 21 24 26 27 29 25 25 30 y X ŷ₁
Amount of fertilizer (x) in pounds for each plot: 12, 5, 15, 17, 20, 14: Bushels of tomatoes harvested (y) 24 22 31 33 21 28: Round all values to three decimal places. a) Find the equation of the regression line (line of best fit). b) Calculate the correlation coefficient (r). c) Determine if there is a significant linear correlation. d) If the linear relation is significant, predict how many bushels of tomatoes would be harvested if 22 pounds of fertilizer was used.
The following table shows the values of the age and the job satisfaction of ice cream shop employees Employee Age Job Satisfaction16 918 920 722 824 426 528 626 524 722 8 d. Sketch a scatterplot of this data by hand (do NOT use/submit any plots created by a program).e. Does there appear to be a linear relationship between the two variables? f. Calculate the slope for this data.
The following table shows students’ number of absences, x, and the student’s final grade,, y.# of absences x 6 2 15 9 12 5 8 Final grade y 82 86 43 74 58 90 78a) Calculate r, the correlation coefficient ________________b) Find the equation of the regression line __________________________________c) If a student is absent 4 times,, what grade does your regression line predict?__________________
d. Draw the regression line on the scatter diagram using the yp points.e. Find y for x = 50 x 20 10 30 40 60 70 y 20 20 30 50 60 80

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