### Understanding Regression Analysis for Language Proficiency ExamsIn 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. Your task is to find the equation of the regression line for the given data.#### Data Table:- **Number of years, x:** - 3, 4, 4, 5, 3, 6, 2, 7- **Grades on test, y:** - 61, 68, 75, 82, 73, 90, 58, 93, 72 #### Options for Regression Line Equation:- **Option A:** - $\hat{y} = 6.910x - 46.261$ - **Option B:** - $\hat{y} = 46.261x + 6.910$ - **Option C:** - $\hat{y} = 6.910x + 46.261$ - **Option D:** - $\hat{y} = 46.261x - 6.910$ #### Explanation:To find the best fit line, or regression line, one typically uses the least squares method, which minimizes the sum of the squared differences between observed and predicted values. The regression equation is typically represented in the form:\[\hat{y} = a + bx\]Where:- $\hat{y}$ is the predicted value.- $a$ is the y-intercept.- $b$ is the slope of the line.#### Conclusion:After assessing the options provided, determine which equation best fits the data by calculating or using statistical software to find the most accurate equation reflecting the relationship between study years and test grades. This guides decisions and predictions related to language proficiency outcomes based on study duration.

Find Regression line equations from the following data X Y 3 61 4 68 4 75 5 82 3 73 6…

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Problem 1P

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The following table gives the data for the grades on the midterm exam and the grades on the final exam. Determine the equation of the regression line, y = bo + b₁x. Round the slope and y-intercept to the nearest thousandth. Grades on Midterm and Final Exams Grades on Midterm 78 70 84 97 82 75 75 88 67 76 89 79 88 100 Grades on Final 71 80 77 77 72 65
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The following are the intelligence quotients (IQ) and the grade point average (GPA) of incoming Grade 12 students. If a significant relationship exists between the variables, perform a regression analysis. What GPA will students A and B obtain if their IQs are 159 and 92, respectively? Support your answer with computations/tables and draw the corresponding scatter diagram. Student IQ GPA 1 153 94 120 87 108 89 135 93 97 85 110 86 155 95 126 88 122 86 10 94 84 23455 6 7 8 9은
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The datasetBody.xlsgives the percent of weight made up of body fat for 100 men as well as other variables such as Age, Weight (lb), Height (in), and circumference (cm) measurements for the Neck, Chest, Abdomen, Ankle, Biceps, and Wrist. We are interested in predicting body fat based on abdomen circumference. Find the equation of the regression line relating to body fat and abdomen circumference. Make a scatter-plot with a regression line. What body fat percent does the line predict for a person with an abdomen circumference of 110 cm? One of the men in the study had an abdomen circumference of 92.4 cm and a body fat of 22.5 percent. Find the residual that corresponds to this observation. Bodyfat Abdomen 32.3 115.6 22.5 92.4 22 86 12.3 85.2 20.5 95.6 22.6 100 28.7 103.1 21.3 89.6 29.9 110.3 21.3 100.5 29.9 100.5 20.4 98.9 16.9 90.3 14.7 83.3 10.8 73.7 26.7 94.9 11.3 86.7 18.1 87.5 8.8 82.8 11.8 83.3 11 83.6 14.9 87 31.9 108.5 17.3…
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KidsFeet Regression Line y-Intercept The KidsFeet dataframe contains data collected on 39 fourth grade students in Ann Arbor, MI, in October 1997. Two of the measurements taken on the children were the length in centimeters, (length), and width in centimeters, (width), of their longest foot. This data could be used to answer the following Research Question: How is the width of a fourth-grade student's foot related to the length? Which of the following is the y-intercept of the regression line? ## ## Simple Linear Regression## ## Correlation coefficient r = 0.6411 ## ## Equation of Regression Line:## ## length = 9.817 + 1.658 * width ## ## Residual Standard Error: s = 1.025 ## R^2 (unadjusted): R^2 = 0.411 ( ) 1.0248 ( ) 1.6576 ( ) 22.8153 ( ) 0.411 ( ) 9.8172 ( )0.6411
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Find the equation of the regression line for the following data: X 23 43 29 32 46 22 37 y 56 8 44 35 13 48 20
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

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