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Solve 4 and XC

Solve 4 and XC

MATLAB: An Introduction with Applications
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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Solve 4 and XC. I attached my answers to the other questions if needed

Since the beginning of the semester, Mr. Bates has regular workouts where his Apple Watch® keeps track of his calories burned. The data for his workouts is in the table on the left side. Minutes Calories 30 293 1. On a separate sheet of paper, graph this data in a scatterplot. Make sure to label your axes. 30 301 26 221 33 331 30 276 21 182 2. Find the correlation coefficient of the data. 29 280 15 93 40 327 31 267 3. Find a linear regression equation to model this data. 32 261 30 265 34 357 21 194 4. If Mr. Bates exercises for 35 minutes, how many calories is he likely to burn? (Round to the nearest whole number). 28 282 XC. If Mr. Bates' watch says he burned 150 calories, how many minutes did he most likely exercise? (Round to the nearest whole number.)
Transcribed Image Text:Since the beginning of the semester, Mr. Bates has regular workouts where his Apple Watch® keeps track of his calories burned. The data for his workouts is in the table on the left side. Minutes Calories 30 293 1. On a separate sheet of paper, graph this data in a scatterplot. Make sure to label your axes. 30 301 26 221 33 331 30 276 21 182 2. Find the correlation coefficient of the data. 29 280 15 93 40 327 31 267 3. Find a linear regression equation to model this data. 32 261 30 265 34 357 21 194 4. If Mr. Bates exercises for 35 minutes, how many calories is he likely to burn? (Round to the nearest whole number). 28 282 XC. If Mr. Bates' watch says he burned 150 calories, how many minutes did he most likely exercise? (Round to the nearest whole number.)
301 221 30 900 90601 9030 Software Procedure: 26 676 48841 5746 33 331 1089 109561 10923 8280 3822 8120 The step-by-step procedure to draw a scatter diagram using EXCEL software is given below: 30 276 900 76176 33124 78400 21 182 441 280 841 • Open an EXCEL file. • Enter the data of Minutes in column A and name it as Minutes. • Enter the data of Calories in column Band name it as Calories. • Select Data and go to Insert tab. • Select Scatter or Bubble chart > Scatter plot. • Click OK. 225 8649 106929 71289 68121 1395 13080 8277 327 1600 267 261 961 1024 8352 7950 70225 127449 37636 79524 y = 3930 Ex = 12838 Ey =1,092,374 30 265 900 1156 441 784 12138 4074 7896 34 357 21 194 28 282 The Scatterplot is shown below: Σχ-430 Ey =117,873 Scatterplot Therefore , the required values are Σχ= 430, Σy= 3930, Σχ12838, Σ) = 1092374 and Σxy 400 117873. 350 Denote ras the sample correlation coefficient between the variables xand y. 300 The correlation coefficient is obtained as given below: 250 200 n(Ew)-(Ex)(Ev) 150 100 (15x117873)-(430 x 3930) 50 (15x12838) - (430) x(15x1092374)-(3930) 5 10 15 20 25 30 35 40 45 = 0.9206 (Rounded to 4 decimal places) Minutes Thus, the correlation coefficient is r= 0.9206. (c). Find the least squares regression equation: The values of x-bar and y-bar are obtained as given below: Ex 430 15 = 28.6667 (Rounded to 4 decimal places) Σν 3930 15 = 262 Regression coefficient: The regression coefficient is obtained as b= 10.1949 from the calculation given below: (Ew)-(Ex)(E») (15x117873)-(430 × 3930) (15 x12838) -(430) =10.1949 (Rounded to 3 decimal places) Therefore, the regression coefficient is b= 10.1949. Intercept: The intercept is obtained as a =-30.254 from the calculation given below: a =j-bx = 262-(10.1949 x 28.6667) = 262 - 292.2541 =-30.2541 (Rounded to 4 decimal places) Therefore, the regression equation is Calories=- 30.2541 + 10.1949* Minutes. Calories
Transcribed Image Text:301 221 30 900 90601 9030 Software Procedure: 26 676 48841 5746 33 331 1089 109561 10923 8280 3822 8120 The step-by-step procedure to draw a scatter diagram using EXCEL software is given below: 30 276 900 76176 33124 78400 21 182 441 280 841 • Open an EXCEL file. • Enter the data of Minutes in column A and name it as Minutes. • Enter the data of Calories in column Band name it as Calories. • Select Data and go to Insert tab. • Select Scatter or Bubble chart > Scatter plot. • Click OK. 225 8649 106929 71289 68121 1395 13080 8277 327 1600 267 261 961 1024 8352 7950 70225 127449 37636 79524 y = 3930 Ex = 12838 Ey =1,092,374 30 265 900 1156 441 784 12138 4074 7896 34 357 21 194 28 282 The Scatterplot is shown below: Σχ-430 Ey =117,873 Scatterplot Therefore , the required values are Σχ= 430, Σy= 3930, Σχ12838, Σ) = 1092374 and Σxy 400 117873. 350 Denote ras the sample correlation coefficient between the variables xand y. 300 The correlation coefficient is obtained as given below: 250 200 n(Ew)-(Ex)(Ev) 150 100 (15x117873)-(430 x 3930) 50 (15x12838) - (430) x(15x1092374)-(3930) 5 10 15 20 25 30 35 40 45 = 0.9206 (Rounded to 4 decimal places) Minutes Thus, the correlation coefficient is r= 0.9206. (c). Find the least squares regression equation: The values of x-bar and y-bar are obtained as given below: Ex 430 15 = 28.6667 (Rounded to 4 decimal places) Σν 3930 15 = 262 Regression coefficient: The regression coefficient is obtained as b= 10.1949 from the calculation given below: (Ew)-(Ex)(E») (15x117873)-(430 × 3930) (15 x12838) -(430) =10.1949 (Rounded to 3 decimal places) Therefore, the regression coefficient is b= 10.1949. Intercept: The intercept is obtained as a =-30.254 from the calculation given below: a =j-bx = 262-(10.1949 x 28.6667) = 262 - 292.2541 =-30.2541 (Rounded to 4 decimal places) Therefore, the regression equation is Calories=- 30.2541 + 10.1949* Minutes. Calories
Expert Solution
Step 1

4.

From part 3, the linear regression equation is Calories=-30.2541+10.1949 Minutes.

The number of calories is he likely to burn Mr. Bates exercises for 35 minutes is,

Calories=-30.2541+10.194935=-30.2541+356.8215=326.5674≈327

Thus, the number of calories is he likely to burn Mr. Bates exercises for 35 minutes is 327 calories.

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