EBK MATLAB: AN INTRODUCTION WITH APPLIC
6th Edition
ISBN: 8220103113663
Author: GILAT
Publisher: YUZU
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Chapter 3, Problem 26P
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Compare the elements of with the value 7.5. Use format long to display the numbers.
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3. Bayesian Inference – Updating Beliefs
A medical test for a rare disease has the following characteristics:
Sensitivity (true positive rate): 99%
Specificity (true negative rate): 98%
The disease occurs in 0.5% of the population.
A patient receives a positive test result.
Questions:
a) Define the relevant events and use Bayes’ Theorem to compute the probability that the patient actually has the disease.b) Explain why the result might seem counterintuitive, despite the high sensitivity and specificity.c) Discuss how prior probabilities influence posterior beliefs in Bayesian inference.d) Suppose a second, independent test with the same accuracy is conducted and is also positive. Update the probability that the patient has the disease.
4. Linear Regression - Model Assumptions and Interpretation
A real estate analyst is studying how house prices (Y) are related to house size in square feet (X). A simple
linear regression model is proposed:
The analyst fits the model and obtains:
•
Ŷ50,000+150X
YBoB₁X + €
•
R² = 0.76
• Residuals show a fan-shaped pattern when plotted against fitted values.
Questions:
a) Interpret the slope coefficient in context.
b) Explain what the R² value tells us about the model's performance.
c) Based on the residual pattern, what regression assumption is likely violated? What might be the
consequence?
d) Suggest at least two remedies to improve the model, based on the residual analysis.
Chapter 3 Solutions
EBK MATLAB: AN INTRODUCTION WITH APPLIC
Ch. 3 - Prob. 1PCh. 3 - For the function y=x4ex, calculate the value of y...Ch. 3 - For the function y=(x+yx+3)(1+2x2)x3 , calculate...Ch. 3 - For the function y=4sinx+6(cos2x+sinx)2 ,...Ch. 3 - The radius, r, of a sphere can be calculated from...Ch. 3 - Prob. 6PCh. 3 - The remaining loan balance, B, of a fixed payment...Ch. 3 - Prob. 8PCh. 3 - Prob. 9PCh. 3 - The angle between two vectors u1=x1i+y1j+z1k and...
Ch. 3 - The following vector is defined in MATLAB: d=[2 4...Ch. 3 - The following two vectors are defined in MATLAB:...Ch. 3 - Define the vector v= [1 3 5 7]. Then use the...Ch. 3 - Define the vector v=[5 4 3 2]. Then use the vector...Ch. 3 - Define x and y as the vectors x= [0.5, 1, 1.5, 2,...Ch. 3 - Define r and s as scalars r = 1.6 × 103 and s =...Ch. 3 - The area of a triangle ABC can be calculated by...Ch. 3 - Prob. 18PCh. 3 - The center of mass, ( x , y, z). of n particles...Ch. 3 - Prob. 20PCh. 3 - The maximum distance s and the maximum height h...Ch. 3 - Use MATLAB to show that the sum of the infinite...Ch. 3 - Use MATLAB to show that the sum of the infinite...Ch. 3 - The natural exponential function can be expressed...Ch. 3 - Show that limx/3sin(x/3)4cos2x1=36 . Do this by...Ch. 3 - Show that limx05sin(6x)4x=7.5. Do this by first...Ch. 3 - The Hazen Williams equation can be used to...Ch. 3 - The monthly lease payment. Pmt, of a new car can...Ch. 3 - Create the following three matrices: A= 537206489...Ch. 3 - Use the matrics A, B, and C from the previous...Ch. 3 - Create a 33 matrix A having random integer values...Ch. 3 - The magic square is an arrangement of numbers in a...Ch. 3 - Solve the following system of three linear...Ch. 3 - Solve the following system of six linear...Ch. 3 - A football stadium has 100.000 seats. In a game...Ch. 3 - A food company manufactures five types of 8-oz...Ch. 3 - The electrical circuit shown consists of resistors...
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