2 simple regression
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This document discusses using simple linear regression to describe relationships between variables in data. It explains that regression finds the linear equation that best describes how a dependent variable (y) changes with an independent variable (x). The equation is the line that minimizes the sum of the squared residuals (deviations from the observed data points). Examples are given of regression analyses conducted to estimate the cost of computer networks based on number of computers, estimate real estate values based on house size, and forecast housing starts based on mortgage rates.
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This document discusses statistical cost estimation techniques, including variable costs, fixed costs, and mixed costs. It explains how to use the scattergraph method and regression analysis to derive a total cost equation and estimate mixed costs. Specifically, it discusses using regression to interpret results like the correlation coefficient, coefficient of determination, and t-statistic. It provides an example of using multiple regression with two predictor variables and interpreting those results. Finally, it discusses potential problems that can occur with regression data like curvilinear costs, outliers, spurious relations, and violating assumptions.
(8) Lesson 9.2
This document provides step-by-step examples for determining a line of best fit from a scatter plot and using the line of best fit to make predictions. It explains how to construct a scatter plot, draw a line that best represents the data, write the equation in slope-intercept form, and use the equation to predict values. The examples illustrate how to find the slope and y-intercept, write the line of best fit equation, and make conjectures for data points not explicitly in the original data set.
Line of best fit lesson
This document provides an overview of line of best fit and linear regression. It defines key concepts like linear regression, residuals, and scatter plots. It explains how to determine the line of best fit for a data set by finding the line that minimizes the sum of the squared residuals. An example is worked through showing how to calculate the line of best fit and make a prediction based on that line. The document emphasizes that linear regression is useful for understanding relationships between variables in fields like business and medical research.
Visual Techniques
Developing visual material can help to recall memory and also be a quick way to show lots of information. Visualization helps us remember (like when we try to picture where we’ve parked our car, and what's in our cupboards when writing a shopping list). We can create diagrams and visual aids depicting module materials and put them up around the house so that we are constantly reminded of our learning
Pre-Calculus Midterm Exam 1 Score ______ ____.docx
Pre-Calculus Midterm Exam
1
Score: ______ / ______
Name: ____________________________
Student Number: ___________________
Short Answer: Type your answer below each question. Show your work.
1 Verify the identity. Show your work.
cot θ ∙ sec θ = csc θ
2 A gas company has the following rate schedule for natural gas usage in single-family residences:
Monthly service charge $8.80
Per therm service charge
1st 25 therms $0.6686/therm
Over 25 therms $0.85870/therm
What is the charge for using 25 therms in one month? Show your work.
What is the charge for using 45 therms in one month? Show your work.
Construct a function that gives the monthly charge C for x therms of gas.
Pre-Calculus Midterm Exam
2
3 The wind chill factor represents the equivalent air temperature at a standard wind speed that would
produce the same heat loss as the given temperature and wind speed. One formula for computing
the equivalent temperature is
W(t) = {
𝑡
33 −
(10.45+10√𝑣−𝑣)(33−𝑡)
2204
33 − 1.5958(33 − 𝑡)
if 0 ≤ v < 1.79
if 1.79 ≤ v < 20
if v ≥ 20
where v represents the wind speed (in meters per second) and t represents the air temperature .
Compute the wind chill for an air temperature of 15°C and a wind speed of 12 meters per second.
(Round the answer to one decimal place.) Show your work.
4 Complete the following:
(a) Use the Leading Coefficient Test to determine the graph's end behavior.
(b) Find the x-intercepts. State whether the graph crosses the x-axis or touches the x-axis
and turns around at each intercept. Show your work.
(c) Find the y-intercept. Show your work.
f(x) = x2(x + 2)
(a).
(b).
(c).
Pre-Calculus Midterm Exam
3
5 For the data set shown by the table,
a. Create a scatter plot for the data. (You do not need to submit the scatter plot)
b. Use the scatter plot to determine whether an exponential function or a logarithmic function is
the best choice for modeling the data.
Number of Homes Built in a Town by Year
6 Verify the identity. Show your work.
(1 + tan2u)(1 - sin2u) = 1
Pre-Calculus Midterm Exam
4
7 Verify the identity. Show your work.
cot2x + csc2x = 2csc2x - 1
8 Verify the identity. Show your work.
1 + sec2xsin2x = sec2x
Pre-Calculus Midterm Exam
5
9 Verify the identity. Show your work.
cos(α - β) - cos(α + β) = 2 sin α sin β
10 The following data represents the normal monthly precipitation for a certain city.
Draw a scatter diagram of the data for one period. (You
Exploring Support Vector Regression - Signals and Systems Project
Our team competed in a Kaggle competition to predict the bike share use as a part of their capital bike share program in Washington DC using a powerful function approximation technique called support vector regression.
SupportVectorRegression
This document summarizes an analysis of using Support Vector Regression (SVR) to predict bike rental data from a bike sharing program in Washington D.C. It begins with an introduction to SVR and the bike rental prediction competition. It then shows that linear regression performs poorly on this non-linear problem. The document explains how SVR maps data into higher dimensions using kernel functions to allow for non-linear fits. It concludes by outlining the derivation of the SVR method using kernel functions to simplify calculations for the regression.
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Pre-Calculus Midterm Exam 1 Score ______ ____.docx
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- 4. Graph of An Exact Relationship y = 1 + 2x x y 1 3 2 5 3 7 4 9 5 11 6 13
- 7. Graph of a Relationship That is NOT Exact Let us assume this relationshipis approximately y = 1 +1.25x x y 1 3 2 2 3 8 4 8 5 11 6 13
- 9. Figure 3.3 Deviations From the Line - deviations + deviations
- 14. Figure 3.5 Computations Required for b 1 and b 0 Totals x i y i x i 2 x i y i 1 3 1 3 2 2 4 4 3 8 9 24 4 8 16 32 5 11 25 55 6 13 36 78 21 45 91 196
- 15. Calculations _ _ b 0 = y – b 1 x =
- 17. We statistical software!
- 19. Pricing a Computer Network ^ y [Cost] = 16594 + 650 [#computers]
- 22. Tarrant County Real Estate ^ y [Value] = -50035 + 72.8 [sq feet]
- 26. US Housing Starts ^ y [starts] = 1726 - 22.2 [rates]
Editor's Notes
- Multiple Regression I