Please tell if I am doing things correctly. Question 1: What is the Pearson correlation r? (report to 2 decimal places) The Pearson correlation coefficient rr is given by the square root of R2R2. Since the provided R2R2 (coefficient of determination) is 89.89%, r=0.8989=0.9481r=0.8989 r =0.9481 The slope sign in the regression equation will determine the r sign. Since the slope is negative, rr will also be negative. r=−0.9481r=−0.9481 Answer: r=−0.95r=−0.95 (rounded to two decimal places) What is the strength of this relationship? Given that the absolute value of rr is 0.95, which is very close to 1, this indicates a very strong linear relationship. Answer: Strong If you use the regression equation to make a prediction, what error or residual would you expect? (report to 3 decimal places) The residual standard error SS represents the typical amount by which the data points deviate from the regression line. It gives a measure of the spread of the residuals about the fitted regression line. The given value of SS is 0.345210. Answer: S=0.345S=0.345 (rounded to three decimal places) Find the residual or error for the specific point with Natural growth rate = -1.39 and Median age = 44.5. (report to 2 decimal places) Using the regression equation: Natural growth rate=4.2464−0.10808×Median ageNatural growth rate=4.2464−0.10808×Median age Plug in the value for Median age: Predicted growth rate=4.2464−0.10808×44.5=4.2464−4.80956=−0.56316Predicted growth rate=4.2464−0.10808×44.5=4.2464−4.80956=−0.56316 Now, find the residual: Residual=Observed growth rate−Predicted growth rateResidual=Observed growth rate−Predicted growth rate Residual=−1.39+0.56316=−0.82684Residual=−1.39+0.56316=−0.82684 Answer: Residual = -0.83 (rounded to two decimal places) Now, compiling all answers: r=−0.95r=−0.95 Strong S=0.345S=0.345 Residual = -0.83

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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Please tell if I am doing things correctly.

Question 1: What is the Pearson correlation r? (report to 2 decimal places) The Pearson correlation coefficient rr is given by the square root of R2R2. Since the provided R2R2 (coefficient of determination) is 89.89%, r=0.8989=0.9481r=0.8989

r =0.9481 The slope sign in the regression equation will determine the r sign. Since the slope is negative, rr will also be negative. r=−0.9481r=−0.9481

Answer: r=−0.95r=−0.95 (rounded to two decimal places)

What is the strength of this relationship? Given that the absolute value of rr is 0.95, which is very close to 1, this indicates a very strong linear relationship.

Answer: Strong

If you use the regression equation to make a prediction, what error or residual would you expect? (report to 3 decimal places) The residual standard error SS represents the typical amount by which the data points deviate from the regression line. It gives a measure of the spread of the residuals about the fitted regression line. The given value of SS is 0.345210.

Answer: S=0.345S=0.345 (rounded to three decimal places)

Find the residual or error for the specific point with Natural growth rate = -1.39 and Median age = 44.5. (report to 2 decimal places) Using the regression equation: Natural growth rate=4.2464−0.10808×Median ageNatural growth rate=4.2464−0.10808×Median age Plug in the value for Median age: Predicted growth rate=4.2464−0.10808×44.5=4.2464−4.80956=−0.56316Predicted growth rate=4.2464−0.10808×44.5=4.2464−4.80956=−0.56316 Now, find the residual: Residual=Observed growth rate−Predicted growth rateResidual=Observed growth rate−Predicted growth rate Residual=−1.39+0.56316=−0.82684Residual=−1.39+0.56316=−0.82684

Answer: Residual = -0.83 (rounded to two decimal places)

Now, compiling all answers:

r=−0.95r=−0.95
Strong
S=0.345S=0.345
Residual = -0.83

Use the following for number 1-4:
Major concerns for many topics such as global climate change and social security benefits include population growth rates and age of the population. The global median age has
increased from just over 20 years in 1970 to just over 30 years in 2022. A report from Age Structure (H. Ritchie and M. Roser) in Our World in Data looked at the relationship
between the median age of a country and the natural growth rate of a country. Countries with lower median age tend to have higher population growth rates. See the graph and
analysis below:
Natural growth rate
3
2
1
-1
-2
10
S
Natural growth rate vs Median age
0.345210
20
Regression Equation
Natural growth rate = 4.2464 -0.10808 Median age
Model Summary
30
R-Sq
89.89%
40
Median age
50
60

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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