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Date
Jan 9, 2024
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Name: Rishabh Singh
Assignment Name: Assignment 12.1 - Logistic Regression Calculations
Screenshots:
Code:
import numpy as np
#define the sigmoid function
def sigmoid(z):
return 1/(1+np.exp(-z))
#define the loiss function for logistic regression
def loss(a,y):
return -(y*np.log(a)+(1-y)*np.log(1-a))
#calculate the cost function J(w,b) to measure how well them model is performing
def j_cost_fn(predictions,labels):
return np.mean([loss(a,y) for a, y in zip(predictions,labels)])
#calculate the gradient of J with respect to w
def calculate_dw(a,y,x):
return (a-y)*x
#cacucalte the average gradient of J with respect to W
def avg_dw(predictions,labels,inputs):
return np.mean([calculate_dw(a,y,x) for a,y,x in zip(predictions,labels,inputs)])
#calculate the gradient of J with respect to b
def calculate_db(a,y):
return a-y
#calculate the average gradient of J with respcet to b
def avg_db(predictions,labels):
return np.mean([calculate_db(a,y) for a ,y in zip(predictions,labels)])
#calculate descent function to update the model parameters (w and b)
def gradient_descent(X,y,w,b,alpha,num_iterations):
for i in range(num_iterations):
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Related Questions
In your biomechanical testing lab, you perform a series of compression tests to determine the relationship
between apparent bone density (p, units of g/cm³) and ultimate stress (ơult, units of MPa). Using the set of
experimental measurements below, write an m-file to fit a power relationship of the form
O uli = Ap
to the data. Use the log transform method to linearize the system and data, followed by linear regression.
Plot the data points and the power relationship on a single plot. Be sure to label your axes and provide a
legend. Provide a printout of your m-file and a printout of the command window showing your results.
Write down the best fit equation and box it.
8.76
5.25
4.26
5.51
3.88
18.45
2.09
13.72
5.42
2.17
Oult (MPa)
p (g/cm³)
0.598 | 0.459
0.319 | 0.235
0.141
0.754
0.177
0.553
0.394
0.246
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As an industrial engineer, you intend to use linear trend (or linear regression) method to solve a forecasting problem. You have decided to use the equation of y = m(x) + c to establish the relationship between the sales (y) and the related month (x). It is known that 8 consecutive months data (Jan to Aug) were used and they resulted to the following parameter values of m = 320 and c = 1017. Using the regression technique, estimate the percentage of sales improvement from December this year to June next year.
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mathforadmi..2dff1dd723
PTU
Kadoorie sygini
1930
Technical
Department of Applied Mathematics
Second Semester 2020/2021
Math for Administration
Assignment 2
Question 1
For the function:
y = 0.01x- 0.001x²
Find the zeros, the vertex and the optimum
value (max. or min.)
Question 2
Suppose a company has fixed costs of $300
and variable
3
costs of x + 1460 dollars per unit,
4
where x is the
total number of units produced. Suppose
further that the
selling price of its product is 1500
X-
♡ lar
Fine break-even points.
init.
II
جامعة
Palestine
||
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a)
b)
c)
Use composite Simpson's rule to estimate xe*dx with n=4.
Subsequently, find the absolute error.
dy
dx
Given 3y + 2x, where y(0) = 1 and h = 0.2.
Approximate the solution for the differential equation for one iteration only by
using Runge Kutta method of order two.
Set up the Gauss-Siedel iterative equations the following linear system:
6x₁-3x₂ = 2
-x₁ + 3x₂ + x3 =1
x₂ + 4x₂ = 3
(Do not solve)
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Q=What is the importance of regression analysis in transportation engineering?
ANSWER in word fomat
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Projects A and B are mutually exclusive. The minimum attractive rate of return (MARR) is 12%.
Using rate of return analysis, which project should be selected?
If the image fails to load here, go to https://www.dropbox.com/s/ld6wctqieu8jgwp/ROR.jpg
Year
0
1
2
3
4
ROR
A
- $750
$200
$200
$200
$600
17.68%
B
- $1,150
$300
$350
$400
$700
16.44%
O Project A
O Project B
O Both Project A and B
O Select none of the project.
O Insufficient information to make a decision.
B-A
- $400
$100
$150
$200
$100
13.69%
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1) Graph 1: plot t on the abscissa versus y on the ordinate and (artistically) draw a smooth line through the points. The line need not actually go through each data point.
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3) On graph (1), what does the slope of the line tell you about the velocity of the ball? Be thorough!
4) On graph 2:
a) What does the slope of the line tell you about the acceleration of the ball? Be thorough!
b) Calculate g from the freefall data and the % error (in comparison to 9.81 m/s^2) using the results from the linear regression calculation.
c) What do the values of the y-intercept and correlation coefficient (r) tell you?
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The orthographic views of an object are
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a) Draw its isometric drawing using a pencil.
Provide all important dimensions on your
isometric drawing.
b) You need to take pictures of all main
steps and need to provide a step-by-step
method to draw isometric drawing
accompanied by pictures.
307303030 |
20
60
15
15
55 30
20
60
+
27.5
4
25
47.5
25
R20
20
T
15
60
016
120
R30
120
120
30
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Table Error function (erf) values
erf (z)
erf (2
erf (z)
0.55
0.5033
13
0.9340
0.025
0.0282
O 60
0.6039
14
0.9523
0.05
0.0564
0.05
0 6420
15
0.9001
0.10
0.1125
0.70
0 6778
0.9703
16
0.15
0.1080
0.75
0.7112
1.7
0.9838
0 20
0.2227
080
07421
18
0.0091
025
0 2703
0.85
0.7707
1.9
0.0028
0.30
0.3290
0.90
0.7969
20
0.9953
0.35
03704
0.95
0.8200
22
0.9981
040
0.4284
O 8427
O 8802
1.0
24
0.9903
0.45
0.4755
11
2.6
0.0098
0 50
0.5205
12
0.9103
28
0 9990
A 1010 steel is to be carburized using a gas atmosphere that produces 1.0% Cat the surface of the steel. The case depth is defined as the distance below the
surface that contains at least 0.5% Č. If carburizing is done at 1000 C, determine the time required to produce a case depth of 0 234 mm. For the diffusion of
Garbon in FCC iron Q - 137.7 kJ/mol and Do = 0.23 x 10 m²/s. The gas constant is R- 8.314 J/(mol - K). Assume that the diffusion coefficient D
remains constant and the concentrations of the diffusing atoms at the surface (c.) and at…
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Parts for each product
Homework 1
n produce dryer
plant Can
for each product
castiens Then each product is assembled in its dedicated
washing and
dryer
A
machines. Difterent
are manufactured by press and
motor
ly sechon. The
the
monthly capacity of different sections are:
washing machine or looo dryer machine
Press section:
100
- Motor section: 1600 washing
machine or 7o00 drjer machine
machine assembly line: goo0 machine
washing
druer machine assembly line: 5000 machine
washing
1, profit for each unct of washing and dryer machines is 270
and 300 respectively. Formulate a
linear programming problem for
Find ing how many washing and dryer machines should be produced
many washing
to maximize
total plant's profit.
2.A
A Post Company need to transfer 30000 boxes with two
each truck presented
of
olifferent trucks. Chavactenistics
problem for
The table below. Formulate a linear programming
each truck to
optimum nunber of minimIze total Cost.
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Regards,Irfan
Mention the types of problems that exist in the field of engineering, especially mechanical engineering that can be solved by the linear regression method
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Table:
Frequency (Hz)
Density (kg/m)
Tension (N)
Speed (cm/s)
Wavelength (cm)
0.85
0.1
4.0
632.5
744.12
0.85
0.7
4.0
239.0
281.18
0.85
1.3
4.0
175.4
206.35
0.85
1.9
4.0
145.1
170.70
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1.00*Exp(0.5x)
Y: 0.4, 1, 4, 36
X: 0.2, 2, 4, 8
y = 1.00e0.06x
All solutions are not correct
O y = 0.35e0.58x
O y = 1.35e1.5x
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docs.google.com/for
3
Your answer
Draw the orthogonal projections of
the Isometric shown in the figure
below.
52
20
26
TRUE R16
12
180
1 Add file
Submit
Never submit passwords through Google Forms.
This form was created inside of University of
Baghdad. Report Abuse
001
Il>
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Student
A
B
D
H
Number
201780130
2
1
7
8
1
3
Evaluate the following variables and use them as given in the following problems.
200 if I is even, 250 if I is odd
(D + G)*10
(H + I/2, if in case the result is zero, use 3
(A +C + E)*2
(P + M)*20
H + 5
M
Q
%3D
50(E + G + 1)
II
II || || || ||||
ZNPORX
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Chapter 4 Homework
Question 5
0/1
Question 13 of 14
-/ 1
Math Fill in the Blank
X Incorrect
Question 6
1/1
v Correct
As shown in the figure, Refrigerant 22 enters the compressor of an air conditioning unit operating at steady state at 40°F, 80 lbf/in?
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separate stream occurs, and the refrigerant exits as a liquid at 200 lb;/in?, 90°F. Air enters the condenser at 70°F, 14.7 Ib;/in? with a
volumetric flow rate of 1000 ft°/min and exits at 110°F. Neglect stray heat transfer and kinetic and…
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For all the following problems,
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a)
b)
You need to show at least 3 iterations calculated manually with all steps.
You do not need to include the M.files for the bisection method (bisect.m) and for false position (falspos.m). You
must, however, show the command lines for the given functions with their variables and other parameters.
Fanning friction factor
For fluid flow in pipes, friction is described by a dimensionless number, the Fanning friction factor
f. The Fanning friction factor is dependent on a number of parameters related to the size of the pipe
and the fluid, which can all be represented by another dimensionless quantity, the Reynolds number
Re. A formula that predicts ƒ given Re is the von Karman equation:
4log₁0 (Re√) - 0.4
=
Typical values for the Reynolds number for turbulent flow are 10,000 to 500,000 and for the
Fanning friction factor are 0.001 to 0.01.
(a) Develop a function that uses bisection to solve for fgiven a user-supplied value of Re between
500 and…
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Forest Fires and Acres Burned Numbers (in thousands) of forest fires over the year and the number (in hundred thousands) of acres burned for 6 recent
years are shown. The regression line equation is y'=-18.779+0.761x. The standard error of the estimate is sest 9.55. Find the 80% interval when x=60.
Round intermediate answers to three decimal places. Round your final answers to two decimal places as needed.
Number of fires x
58
47
84
62
57
45
Number of acres burned y
19
26
51
15
30
15
Send data to Excel
One can be 80% confident that the interval
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4. Given the following data :
T(k')
600
700
800
900
(Cp/R)
3.671
3.755
3.838
3.917
Where "T" is the absolute temperature and (C,/R) is the dimensionless specific heat of
air. Use Newton's forward interpolation method to find the specific heat at T = 670 k°.
%3D
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4.
Develop a model using regression analysis for trip production using the following data.
Zone Number
Trip production
Trip
Vehicle
Employment
attraction
ownership
1
200
1
1000
256
1.5
1250
345
2500
6.
451
2.8
3600
5
6.5
555
4200
6.
7
600
4
4500
3.
2.
3.
2.
3.
4.
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For the Thermistor given below using
piecewise approximation method
combined with line regression to find
the best equation and value for
Temperature if the system has
counts =800
20
40
60
80
|ADC counts
928
785
654
420
152
T=129.7902-0.14586*Counts, T=
13.1022
T=129.7902-0.13986*Counts,
T=17.9021
T=129.7902-0.12358*Counts, T=
30.9262
T=135.4745-0.14599*Counts, T=
18.68613
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Q1: The number of bacterial cells (P) in a given reactor is related to time in
days (t) as described by the following mathematical model:
dp
dt
0.0000007 P², If at initial time (P = 106). Determine the
number of cells when (t 2days) using the fourth order Runge-Kutta
method and at time increment of (1 day).
=
= 0.3 P
1
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computational methods - linear regression
do not use spreadsheet program to find answer.
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5
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CENGAGE MINDTAP
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Chapter 5: Review Questions
Assignment: Chapter 5: Review Questions (Practice)
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If a planet were to slowly migrate inward toward the Sun while remaining in a stable orbit, would its orbital speed increase, decrease, or stay the same? Would its angular momentum change?
O
a. As the planet migrates toward the Sun, its orbital speed would increase and its angular momentum would decrease.
b. As the planet migrates toward the Sun, its orbital speed would stay the same and its angular momentum would decrease.
OC. As the planet migrates toward the Sun, its orbital speed would increase and its angular momentum would stay the same.
Od. As the planet migrates toward the Sun, its orbital speed and angular momentum would stay…
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What can surrogate models enable? Check all that apply.
They can help linearize strongly nonlinear forward models.
They can help accelerate evaluation of the forward model or likelihood in Bayesian inference.
They can make it easier to exploit parallel computing resources.
They can reduce the dimensionality of the data.
They can help push more computation to an "offline" phase of the analysis.
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Problem 2: Note: Make sure to show all steps and work done in order to get the full credit.
A set of experimental data is given as:
x 0.4
0.8
1.6
2.3
800
980
1945 3600
Use a straight line to fit the data. y = ao + a,x. Find its coefficients
Find standard deviation for the linear regression.
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Related Questions
- In your biomechanical testing lab, you perform a series of compression tests to determine the relationship between apparent bone density (p, units of g/cm³) and ultimate stress (ơult, units of MPa). Using the set of experimental measurements below, write an m-file to fit a power relationship of the form O uli = Ap to the data. Use the log transform method to linearize the system and data, followed by linear regression. Plot the data points and the power relationship on a single plot. Be sure to label your axes and provide a legend. Provide a printout of your m-file and a printout of the command window showing your results. Write down the best fit equation and box it. 8.76 5.25 4.26 5.51 3.88 18.45 2.09 13.72 5.42 2.17 Oult (MPa) p (g/cm³) 0.598 | 0.459 0.319 | 0.235 0.141 0.754 0.177 0.553 0.394 0.246arrow_forwardAs an industrial engineer, you intend to use linear trend (or linear regression) method to solve a forecasting problem. You have decided to use the equation of y = m(x) + c to establish the relationship between the sales (y) and the related month (x). It is known that 8 consecutive months data (Jan to Aug) were used and they resulted to the following parameter values of m = 320 and c = 1017. Using the regression technique, estimate the percentage of sales improvement from December this year to June next year.arrow_forwardmathforadmi..2dff1dd723 PTU Kadoorie sygini 1930 Technical Department of Applied Mathematics Second Semester 2020/2021 Math for Administration Assignment 2 Question 1 For the function: y = 0.01x- 0.001x² Find the zeros, the vertex and the optimum value (max. or min.) Question 2 Suppose a company has fixed costs of $300 and variable 3 costs of x + 1460 dollars per unit, 4 where x is the total number of units produced. Suppose further that the selling price of its product is 1500 X- ♡ lar Fine break-even points. init. II جامعة Palestine ||arrow_forward
- a) b) c) Use composite Simpson's rule to estimate xe*dx with n=4. Subsequently, find the absolute error. dy dx Given 3y + 2x, where y(0) = 1 and h = 0.2. Approximate the solution for the differential equation for one iteration only by using Runge Kutta method of order two. Set up the Gauss-Siedel iterative equations the following linear system: 6x₁-3x₂ = 2 -x₁ + 3x₂ + x3 =1 x₂ + 4x₂ = 3 (Do not solve)arrow_forwardQ=What is the importance of regression analysis in transportation engineering? ANSWER in word fomatarrow_forwardProjects A and B are mutually exclusive. The minimum attractive rate of return (MARR) is 12%. Using rate of return analysis, which project should be selected? If the image fails to load here, go to https://www.dropbox.com/s/ld6wctqieu8jgwp/ROR.jpg Year 0 1 2 3 4 ROR A - $750 $200 $200 $200 $600 17.68% B - $1,150 $300 $350 $400 $700 16.44% O Project A O Project B O Both Project A and B O Select none of the project. O Insufficient information to make a decision. B-A - $400 $100 $150 $200 $100 13.69%arrow_forward
- 1) Graph 1: plot t on the abscissa versus y on the ordinate and (artistically) draw a smooth line through the points. The line need not actually go through each data point. 2) Graph 2: plot t^2 on the abscissa versus y on the ordinate and then perform a linear regression. Remember to plot both the raw data points and the line of best fit (with the two points used to draw it); also show the regression equation and r value on the graph. 3) On graph (1), what does the slope of the line tell you about the velocity of the ball? Be thorough! 4) On graph 2: a) What does the slope of the line tell you about the acceleration of the ball? Be thorough! b) Calculate g from the freefall data and the % error (in comparison to 9.81 m/s^2) using the results from the linear regression calculation. c) What do the values of the y-intercept and correlation coefficient (r) tell you?arrow_forwardThe orthographic views of an object are shown below. a) Draw its isometric drawing using a pencil. Provide all important dimensions on your isometric drawing. b) You need to take pictures of all main steps and need to provide a step-by-step method to draw isometric drawing accompanied by pictures. 307303030 | 20 60 15 15 55 30 20 60 + 27.5 4 25 47.5 25 R20 20 T 15 60 016 120 R30 120 120 30arrow_forwardTable Error function (erf) values erf (z) erf (2 erf (z) 0.55 0.5033 13 0.9340 0.025 0.0282 O 60 0.6039 14 0.9523 0.05 0.0564 0.05 0 6420 15 0.9001 0.10 0.1125 0.70 0 6778 0.9703 16 0.15 0.1080 0.75 0.7112 1.7 0.9838 0 20 0.2227 080 07421 18 0.0091 025 0 2703 0.85 0.7707 1.9 0.0028 0.30 0.3290 0.90 0.7969 20 0.9953 0.35 03704 0.95 0.8200 22 0.9981 040 0.4284 O 8427 O 8802 1.0 24 0.9903 0.45 0.4755 11 2.6 0.0098 0 50 0.5205 12 0.9103 28 0 9990 A 1010 steel is to be carburized using a gas atmosphere that produces 1.0% Cat the surface of the steel. The case depth is defined as the distance below the surface that contains at least 0.5% Č. If carburizing is done at 1000 C, determine the time required to produce a case depth of 0 234 mm. For the diffusion of Garbon in FCC iron Q - 137.7 kJ/mol and Do = 0.23 x 10 m²/s. The gas constant is R- 8.314 J/(mol - K). Assume that the diffusion coefficient D remains constant and the concentrations of the diffusing atoms at the surface (c.) and at…arrow_forward
- Parts for each product Homework 1 n produce dryer plant Can for each product castiens Then each product is assembled in its dedicated washing and dryer A machines. Difterent are manufactured by press and motor ly sechon. The the monthly capacity of different sections are: washing machine or looo dryer machine Press section: 100 - Motor section: 1600 washing machine or 7o00 drjer machine machine assembly line: goo0 machine washing druer machine assembly line: 5000 machine washing 1, profit for each unct of washing and dryer machines is 270 and 300 respectively. Formulate a linear programming problem for Find ing how many washing and dryer machines should be produced many washing to maximize total plant's profit. 2.A A Post Company need to transfer 30000 boxes with two each truck presented of olifferent trucks. Chavactenistics problem for The table below. Formulate a linear programming each truck to optimum nunber of minimIze total Cost.arrow_forwardHello Sir.Good night.Permission, i have a question in my homework related numerical methods lesson. The following bellow is question. Please advice. Thank you so much Regards,Irfan Mention the types of problems that exist in the field of engineering, especially mechanical engineering that can be solved by the linear regression methodarrow_forwardWhat mathematical relationship exists between the wave speed and the density of the medium, using the POWER trendline equation from the graph? Make your response specific (i.e., describe the full mathematical proportionality between the two variables) Feel free to use the table. Table: Frequency (Hz) Density (kg/m) Tension (N) Speed (cm/s) Wavelength (cm) 0.85 0.1 4.0 632.5 744.12 0.85 0.7 4.0 239.0 281.18 0.85 1.3 4.0 175.4 206.35 0.85 1.9 4.0 145.1 170.70arrow_forward
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Mechanical Engineering
ISBN:9781259822674
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Control Systems Engineering
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Publisher:WILEY
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ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
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Author:James L. Meriam, L. G. Kraige, J. N. Bolton
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