**Title: Understanding Linear Regression: A Practical Example****Introduction**You are the foreman of the Bar-S cattle ranch in Colorado. A neighboring ranch has calves for sale, and you are interested in purchasing some to add to your herd. To determine the appropriate weight for a healthy calf, we will use linear regression. Let $ x $ represent the age of the calf in weeks, and $ y $ represent the weight of the calf in kilograms. The following table provides the data:| x (weeks) | 2 | 4 | 9 | 16 | 26 | 36 ||-----------|---|---|---|----|----|----|| y (kg) | 37| 51| 78| 100| 150| 200|**Task 1: Verify the Given Sums**Calculate and verify the following:- $\sum x$- $\sum y$- $\sum x^2$- $\sum y^2$- $\sum xy$Determine the sample correlation coefficient $ r $ and round it to four decimal places.**Task 2: Least-Squares Line Equation**Compute the mean values $\bar{x}$ and $\bar{y}$, then find the equation of the least-squares line $\hat{y} = a + bx$. Round your answers to four decimal places.**Task 3: Coefficient of Determination**Calculate the coefficient of determination $ r^2 $. Determine the percentage of variation in $ y $ that is explained by the variation in $ x $ and the least-squares line. Also, find the percentage of variation that is unexplained. Round $ r^2 $ to four decimal places and the percentages to two decimal places.**Predicting the Weight**For calves aged 18 weeks, use the least-squares line to predict a healthy weight. Round your answer to two decimal places. **Conclusion**This exercise demonstrates how linear regression can be used to make predictions and understand relationships between variables in a practical setting, such as ranching.

Given observation and calculation X Y XY X2 Y2 2 37 74 4 1369 4 51…

You are the foreman of the Bar-S cattle ranch in Colorado. A neighboring ranch has calves for sale, and you are going to buy some calves to add to the Bar-S herd. How much should a healthy calf weigh? Let x be the age of the calf (in weeks), and let y be the weight of the calf (in kilograms). 26 150 36 200 16 4 51 78 37 100 Verify the given sums Ex, Ey, Ex², Ey², Exy, and the value of the sample correlation coefficient r. (Round your value for r to four decimal places.) Ex = Ey = Ex? = Ey? = Exy = Find x, and y. Then find the equation of the least-squares line ŷ = a + bx. (Round your answers to four decimal places.) y = ŷ = Find the value of the coefficient of determination 2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for to four decimal places. Round your answers for the percentages to two decimal place.) explained % unexplained % The calves you want to buy are 18 weeks old. What does the least-squares line predict for a healthy weight? (Round your answer to two decimal places.) kg

You are the foreman of the Bar-S cattle ranch in Colorado. A neighboring ranch has calves for sale, and you are going to buy some calves to add to the Bar-S herd. How much should a healthy calf weigh? Let x be the age of the calf (in weeks), and let y be the weight of the calf (in kilograms). 26 150 36 200 16 4 51 78 37 100 Verify the given sums Ex, Ey, Ex², Ey², Exy, and the value of the sample correlation coefficient r. (Round your value for r to four decimal places.) Ex = Ey = Ex? = Ey? = Exy = Find x, and y. Then find the equation of the least-squares line ŷ = a + bx. (Round your answers to four decimal places.) y = ŷ = Find the value of the coefficient of determination 2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for to four decimal places. Round your answers for the percentages to two decimal place.) explained % unexplained % The calves you want to buy are 18 weeks old. What does the least-squares line predict for a healthy weight? (Round your answer to two decimal places.) kg

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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