Dealing with heteroscedasticity additional material 2
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The document provides steps to test for heteroscedasticity in regression analysis. It describes estimating a regression model using GDP, investment, and unemployment. Residual plots and tests, including Breusch-Pagan Godfrey and White tests, are used to check if the variance of the error terms increases with predicted values, which would indicate heteroscedasticity. Both tests find significant p-values, rejecting the null hypothesis of homoscedasticity and concluding heteroscedasticity is present.
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Fai alshammariChapter 2Section 2.1 Q1- Consider the gr.docx
Fai alshammari
Chapter 2
Section 2.1
Q1:- Consider the graph to the right. Explain the idea of a critical value. Then determine which x-values are critical values, and state why.
Q2:-
Find the relative extreme points of the function, if they exist. Then sketch a graph of the function.
f(x)equals=x squared plus 6 x plus 15x2+6x+15
Q3:-
Find the relative extreme points of the function, if they exist. Then sketch a graph of the function.
G(x)equals=x cubed minus 9 x squared plus 1x3−9x2+1
· Identify all the relative minimum points. Select the correct choice below and, if necessary, fill in the answer box to complete your choice
· Identify all the relative maximum points. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
·
· Graph the function. Choose the correct graph below.
SECTION 2.2
Q1:-
Find all relative extrema and classify each as a maximum or minimum. Use the second-derivative test where possible.
f(x)equals=negative 27 x cubed plus 9 x plus 2−27x3+9x+2
_Identify all the relative minima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
_Identify all the relative maxima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice
Q2:-
Sketch the graph of the following function. List the coordinates of where extrema or points of inflection occur. State where the function is increasing or decreasing as well as where it is concave up or concave down.
f left parenthesis x right parenthesisf(x)equals=x Superscript 4 Baseline minus 4 x cubed plus 3x4−4x3+3
_What are the coordinates of the relative extrema? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
_Identify all the relative maxima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
_On what interval(s) is f increasing or decreasing?
_On what interval(s) is f concave up or concave down?
_ SKETCH GRAPH
Q3:-
Sketch the graph that possesses the characteristics listed.
f is concave
up at
(negative 1−1,66),
concave
downdown
at
(77,negative 4−4),
and has an inflection point at left parenthesis 3 comma 1 right parenthesis .(3,1).
SECTION 2.3
Q1:-
Determine the vertical asymptote(s) of the following function. If none exist, state that fact.
f(x)equals=StartFraction x plus 3 Over x squared plus 9 x plus 18 EndFractionx+3x2+9x+18
Q2:-
Determine the horizontal asymptote of the function.
f(x)equals=StartFraction 8 x cubed minus 8 x plus 3 Over 10 x cubed plus 4 x minus 7 EndFraction8x3−8x+310x3+4x−7
Q3:-
Sketch the graph of the function. Indicate where each function is increasing or decreasing, where any relative extrema occur, where asymptotes occur, where the graph is concave up or concave down, where any points of inflection occur, and where any intercepts occur.
f(x)equ ...
How to manually equalize the histograms of two (or more) subvolumes, measured...
How to manually equalize the histograms of two (or more) subvolumes, measured...Javier García Molleja
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1. Open both subvolumes in ImageJ and identify overlapping slices between them.
2. Duplicate the overlapping slices and obtain histograms to adjust brightness/contrast values iteratively until the histograms are equalized.
3. Convert both subvolumes to 8-bit, apply the brightness/contrast values to equalize the histograms, and concatenate the subvolumes into a single volume.Collect 50 or more paired quantitative data items. You may use a met.pdf
Collect 50 or more paired quantitative data items. You may use a method similar to the Module 1
discussion to collect and enter data into StatCrunch. You will enter the explanatory variable (x-
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a.) Using StatCrunch, compute the sample linear correlation coefficient, R. The Technology
Step-by-Step box at the end of Section 4.1 (page 194) explains how to do so. Do not forget the
video explanation in the Module Notes, if you need it.
b.) Using StatCrunch, find the least-squares regression line equation and plot the scatter diagram,
along with the line. Page 207 (Technology Step-by-Step box) explains how to determine such a
linear equation using StatCrunch. Please note: In order to plot the scatter diagram along with the
line, before clicking Calculate in step 3 of page 207, scroll down to Graphs and make sure Fitted
line plot is selected. Then click Calculate. Then click the right-arrow at the very bottom right
hand side of the results page for the scatter diagram and regression line plot. For an example of
the steps taken and what to expect, click here.
c.) Paste your scatter diagram (with the regression line drawn) and StatCrunch results in the
discussion (by clicking on Options and then Copy. Use Ctrl V to paste it into the discussions).
Try not to use the same data set that another student in the class has used, so your results will be
unique. Make sure your data set is large enough (50 items).
d.) Then, answer the following two questions:
What type of correlation do you observe between the two variables? For ideas, see Figure 4 on
page 181 (Section 4.1).
Would you recommend using this linear model to make predictions about the y-value for a given
x-value? Why or why not?
Solution
Technology Step-by-Step Using StatCrunch:
------------------------------------------------------
Section 1.3 Simple Random Sampling
...........................................................
1. Select Data, highlight Simulate Data, then highlight
Discrete Uniform.
2. Fill in the following window with the appropriate
values. To obtain a simple random sample for the
situation in Example 2, we would enter the values
shown in the figure. The reason we generate 10 rows
of data (instead of 5) is in case any of the random
numbers repeat. Select Simulate, and the random
numbers will appear in the spreadsheet. Note: You
could also select the single dynamic seed radio
button, if you like, to set the seed.
Section 2.1 Drawing Bar Graphs and Pie Charts
Frequency or Relative Frequency Distributions from Raw Data
.....................................................................................................
1. Enter the raw data into the spreadsheet. Name the column variable.
2. Select Stat, highlight Tables, and select Frequency.
3. Click on the variable you wish to summarize and click Calculate.
Bar Graphs from Summarized Data
...............................................................
MATH 533 Education Specialist / snaptutorial.com
This document outlines the contents of the MATH 533 course, including homework assignments, quizzes, discussion questions, and projects for each week, as well as two final exam sets. Key elements covered include statistics, probability, hypothesis testing, confidence intervals, regression, and correlation. Completing all elements would provide comprehensive coverage of statistical analysis techniques and applications.
PAGE 1 Chapter 5 Normal Probability Distributions .docx
PAGE 1
Chapter 5: Normal Probability Distributions
Section 5.1: Intro to Normal Distributions and the Standard Normal Distributions
Objectives:
Normal Distribution Properties
Use z-scores to Calculate Area Under the Standard Normal Curve (using StatCrunch or Calculator)
Discuss Unusual Values
In this section we will revisit histograms which can be estimated with normal (symmetric, bell-shaped) curves. From
Test 1 remember that normal curves have z-scores (for any data value) and areas under the curve (one way: Empirical
Rule). Now we will use these normal curves to find probabilities (areas) and z-scores for any data value. Why do we
need to study this? Eventually we will use these probabilities and z-scores to make decisions.
By using the normal distribution curve, we are treating the data as a continuous random variable that has its own
continuous probability distribution. (Remember that any probability distribution has two properties: all probabilities
are between 0 and 1 and the sum of the probabilities is 1.) **Probabilities = Areas under the curve**
Ex: Consider the normal distribution curves below. Which normal curve has the greatest mean? Which normal curve has
the greatest standard deviation?
Note: Every normal distribution can be transformed into the Standard Normal Distribution (the distribution for z-
scores). This means we will use the z-score formula to transform any data value into a “measure of position” with the
formula:
data value mean
standard deviation
z
PAGE 2
**All probability calculations will be done with either StatCrunch or the TI 83/84 calculator. You do NOT need to learn
how to read the Standard Normal Table.**
**Also < and are treated the same as well as > and for any continuous probability distribution.**
Ex: Confirm that the area to the left of z = 1.15 is 0.8749. **Label the z-score and the area.**
StatCrunch: Stat menu, Calculators, Normal, enter inequality symbol and z-score, Compute
TI-83/84: 2nd VARS normalcdf( -1000000000 Comma 1.15 Comma 0 Comma 1 enter
P(z 1.15) = 0.8749
Ex: Confirm that the cumulative area that corresponds to z = -0.24 is 0.4052. **Label the z-score and the area.**
StatCrunch: Stat menu, Calculators, Normal, Standard, enter inequality symbol and z-score, Compute
TI-83/84: 2nd VARS normalcdf( -1000000000 Comma -0.24 Comma 0 Comma 1 enter
P(z -0.24) = 0.4052
PAGE 3
Ex: Find the area to right of each z-score. Hint: Use the fact that the total area (probability) is 1. **Label the z-score and
the area.**
a) b)
P(z 1.15) = _________________ P(z -0.24) = _________________
Ex: Find the shaded area. **Label the z-score and the area.**
StatCrunch: Stat menu, Calculators, Normal, Stand.
2.6b scatter plots and lines of best fit
This document provides instructions for using a graphing calculator to perform linear regression on a dataset and find the line of best fit. It describes entering paired x and y data values into separate lists, using the LinReg(ax+b) function to determine the regression equation, optionally creating a scatter plot of the original data and regression line, and using the line equation to forecast values. As an example, it analyzes a dataset of alternative-fueled vehicles in the US from 1997 to predict the number in 2014.
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Granger Causality Test: A Useful Descriptive Tool for Time Series Data
Granger Causality Test: A Useful Descriptive Tool for Time Series Data
Similar to Dealing with heteroscedasticity additional material 2
Material 1 introduction to eviews
The document provides step-by-step instructions for using Eviews software to open files, examine variables, create graphs and descriptive statistics, perform regressions, and check residuals. It explains how to open Eviews and files, select variables, view spreadsheet and graph outputs, copy and paste tables and graphs, and estimate equations to analyze relationships between economic variables like GDP, unemployment, and investment. Descriptive statistics, correlations, and regression results are generated and their outputs are viewed, copied, and saved.
Fai alshammariChapter 2Section 2.1 Q1- Consider the gr.docx
Fai alshammari
Chapter 2
Section 2.1
Q1:- Consider the graph to the right. Explain the idea of a critical value. Then determine which x-values are critical values, and state why.
Q2:-
Find the relative extreme points of the function, if they exist. Then sketch a graph of the function.
f(x)equals=x squared plus 6 x plus 15x2+6x+15
Q3:-
Find the relative extreme points of the function, if they exist. Then sketch a graph of the function.
G(x)equals=x cubed minus 9 x squared plus 1x3−9x2+1
· Identify all the relative minimum points. Select the correct choice below and, if necessary, fill in the answer box to complete your choice
· Identify all the relative maximum points. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
·
· Graph the function. Choose the correct graph below.
SECTION 2.2
Q1:-
Find all relative extrema and classify each as a maximum or minimum. Use the second-derivative test where possible.
f(x)equals=negative 27 x cubed plus 9 x plus 2−27x3+9x+2
_Identify all the relative minima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
_Identify all the relative maxima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice
Q2:-
Sketch the graph of the following function. List the coordinates of where extrema or points of inflection occur. State where the function is increasing or decreasing as well as where it is concave up or concave down.
f left parenthesis x right parenthesisf(x)equals=x Superscript 4 Baseline minus 4 x cubed plus 3x4−4x3+3
_What are the coordinates of the relative extrema? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
_Identify all the relative maxima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
_On what interval(s) is f increasing or decreasing?
_On what interval(s) is f concave up or concave down?
_ SKETCH GRAPH
Q3:-
Sketch the graph that possesses the characteristics listed.
f is concave
up at
(negative 1−1,66),
concave
downdown
at
(77,negative 4−4),
and has an inflection point at left parenthesis 3 comma 1 right parenthesis .(3,1).
SECTION 2.3
Q1:-
Determine the vertical asymptote(s) of the following function. If none exist, state that fact.
f(x)equals=StartFraction x plus 3 Over x squared plus 9 x plus 18 EndFractionx+3x2+9x+18
Q2:-
Determine the horizontal asymptote of the function.
f(x)equals=StartFraction 8 x cubed minus 8 x plus 3 Over 10 x cubed plus 4 x minus 7 EndFraction8x3−8x+310x3+4x−7
Q3:-
Sketch the graph of the function. Indicate where each function is increasing or decreasing, where any relative extrema occur, where asymptotes occur, where the graph is concave up or concave down, where any points of inflection occur, and where any intercepts occur.
f(x)equ ...
How to manually equalize the histograms of two (or more) subvolumes, measured...
How to manually equalize the histograms of two (or more) subvolumes, measured...Javier García Molleja
This document provides instructions for manually equalizing the histograms of two X-ray computed tomography (XCT) subvolumes measured under similar conditions using ImageJ software. The key steps are:
1. Open both subvolumes in ImageJ and identify overlapping slices between them.
2. Duplicate the overlapping slices and obtain histograms to adjust brightness/contrast values iteratively until the histograms are equalized.
3. Convert both subvolumes to 8-bit, apply the brightness/contrast values to equalize the histograms, and concatenate the subvolumes into a single volume.Collect 50 or more paired quantitative data items. You may use a met.pdf
Collect 50 or more paired quantitative data items. You may use a method similar to the Module 1
discussion to collect and enter data into StatCrunch. You will enter the explanatory variable (x-
value) in column var1. Then, enter the response variable (y-value) in column var2.
a.) Using StatCrunch, compute the sample linear correlation coefficient, R. The Technology
Step-by-Step box at the end of Section 4.1 (page 194) explains how to do so. Do not forget the
video explanation in the Module Notes, if you need it.
b.) Using StatCrunch, find the least-squares regression line equation and plot the scatter diagram,
along with the line. Page 207 (Technology Step-by-Step box) explains how to determine such a
linear equation using StatCrunch. Please note: In order to plot the scatter diagram along with the
line, before clicking Calculate in step 3 of page 207, scroll down to Graphs and make sure Fitted
line plot is selected. Then click Calculate. Then click the right-arrow at the very bottom right
hand side of the results page for the scatter diagram and regression line plot. For an example of
the steps taken and what to expect, click here.
c.) Paste your scatter diagram (with the regression line drawn) and StatCrunch results in the
discussion (by clicking on Options and then Copy. Use Ctrl V to paste it into the discussions).
Try not to use the same data set that another student in the class has used, so your results will be
unique. Make sure your data set is large enough (50 items).
d.) Then, answer the following two questions:
What type of correlation do you observe between the two variables? For ideas, see Figure 4 on
page 181 (Section 4.1).
Would you recommend using this linear model to make predictions about the y-value for a given
x-value? Why or why not?
Solution
Technology Step-by-Step Using StatCrunch:
------------------------------------------------------
Section 1.3 Simple Random Sampling
...........................................................
1. Select Data, highlight Simulate Data, then highlight
Discrete Uniform.
2. Fill in the following window with the appropriate
values. To obtain a simple random sample for the
situation in Example 2, we would enter the values
shown in the figure. The reason we generate 10 rows
of data (instead of 5) is in case any of the random
numbers repeat. Select Simulate, and the random
numbers will appear in the spreadsheet. Note: You
could also select the single dynamic seed radio
button, if you like, to set the seed.
Section 2.1 Drawing Bar Graphs and Pie Charts
Frequency or Relative Frequency Distributions from Raw Data
.....................................................................................................
1. Enter the raw data into the spreadsheet. Name the column variable.
2. Select Stat, highlight Tables, and select Frequency.
3. Click on the variable you wish to summarize and click Calculate.
Bar Graphs from Summarized Data
...............................................................
MATH 533 Education Specialist / snaptutorial.com
This document outlines the contents of the MATH 533 course, including homework assignments, quizzes, discussion questions, and projects for each week, as well as two final exam sets. Key elements covered include statistics, probability, hypothesis testing, confidence intervals, regression, and correlation. Completing all elements would provide comprehensive coverage of statistical analysis techniques and applications.
PAGE 1 Chapter 5 Normal Probability Distributions .docx
PAGE 1
Chapter 5: Normal Probability Distributions
Section 5.1: Intro to Normal Distributions and the Standard Normal Distributions
Objectives:
Normal Distribution Properties
Use z-scores to Calculate Area Under the Standard Normal Curve (using StatCrunch or Calculator)
Discuss Unusual Values
In this section we will revisit histograms which can be estimated with normal (symmetric, bell-shaped) curves. From
Test 1 remember that normal curves have z-scores (for any data value) and areas under the curve (one way: Empirical
Rule). Now we will use these normal curves to find probabilities (areas) and z-scores for any data value. Why do we
need to study this? Eventually we will use these probabilities and z-scores to make decisions.
By using the normal distribution curve, we are treating the data as a continuous random variable that has its own
continuous probability distribution. (Remember that any probability distribution has two properties: all probabilities
are between 0 and 1 and the sum of the probabilities is 1.) **Probabilities = Areas under the curve**
Ex: Consider the normal distribution curves below. Which normal curve has the greatest mean? Which normal curve has
the greatest standard deviation?
Note: Every normal distribution can be transformed into the Standard Normal Distribution (the distribution for z-
scores). This means we will use the z-score formula to transform any data value into a “measure of position” with the
formula:
data value mean
standard deviation
z
PAGE 2
**All probability calculations will be done with either StatCrunch or the TI 83/84 calculator. You do NOT need to learn
how to read the Standard Normal Table.**
**Also < and are treated the same as well as > and for any continuous probability distribution.**
Ex: Confirm that the area to the left of z = 1.15 is 0.8749. **Label the z-score and the area.**
StatCrunch: Stat menu, Calculators, Normal, enter inequality symbol and z-score, Compute
TI-83/84: 2nd VARS normalcdf( -1000000000 Comma 1.15 Comma 0 Comma 1 enter
P(z 1.15) = 0.8749
Ex: Confirm that the cumulative area that corresponds to z = -0.24 is 0.4052. **Label the z-score and the area.**
StatCrunch: Stat menu, Calculators, Normal, Standard, enter inequality symbol and z-score, Compute
TI-83/84: 2nd VARS normalcdf( -1000000000 Comma -0.24 Comma 0 Comma 1 enter
P(z -0.24) = 0.4052
PAGE 3
Ex: Find the area to right of each z-score. Hint: Use the fact that the total area (probability) is 1. **Label the z-score and
the area.**
a) b)
P(z 1.15) = _________________ P(z -0.24) = _________________
Ex: Find the shaded area. **Label the z-score and the area.**
StatCrunch: Stat menu, Calculators, Normal, Stand.
2.6b scatter plots and lines of best fit
This document provides instructions for using a graphing calculator to perform linear regression on a dataset and find the line of best fit. It describes entering paired x and y data values into separate lists, using the LinReg(ax+b) function to determine the regression equation, optionally creating a scatter plot of the original data and regression line, and using the line equation to forecast values. As an example, it analyzes a dataset of alternative-fueled vehicles in the US from 1997 to predict the number in 2014.
MATH 533 RANK Inspiring Innovation--math533rank.com
MATH 533 Entire Course (New)
FOR MORE CLASSES VISIT
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MATH 533 Week 1 Homework
MATH 533 Week 1 Quiz
MATH 533 Entire Course NEW
Check this A+ tutorial guideline at
https://www.uopassignments.com/math-533-devry
For more classes visit
http://www.uopassignments.com
Instructions(1) Work through the pages below.(2) Use the us_demog.docx
Instructions:(1) Work through the pages below.(2) Use the us_demographics.jmp data table to: (a) select a continuous variable and generate a histogram
(b) select two continuous variables and determine the correlation coefficient(c) generate box plots using College Degrees as the Y, Response variable and Region as the X, Factor variable(3) Copy and paste the results for 2 (a, b, & c) in a Word document.
Histograms, Descriptive Statistics, and Stem and Leaf
Use to display and describe the distribution of continuous (numeric) variables. Histograms and stem and leaf plots allow you to quickly assess the shape, centering and spread of a distribution. For categorical (nominal or ordinal) variables, see the page on Bar Charts and Frequency Distributions.
Histograms and Descriptive Statistics
1. Open the JMP® data table us_demographics.jmp, select Analyze > Distribution.
2. Click on one of the continuous variables from Select Columns, and click Y, Columns (continuous variables have blue triangles).
3. Click OK to generate a histogram, outlier box plot and descriptive statistics.
· The percentiles, including quartiles and the median, are listed under Quantiles.
· The sample mean, standard deviation and other statistics are listed under Summary Statistics.
Example: Car Physical Data.jmp (Help > Sample Data)
Tips:
· To change the display from vertical to horizontal (as shown), click on the top red triangle and select Stack.
· To change the graphical display for a variable, or to select additional options, click on the red triangle for that variable.
· To display different summary statistics, use the red triangle next to Summary Statistics.
· To change all future output to horizontal, go to Preferences > Platforms > Distribution, click Stack and
Horizontal, then click OK.
Stem and Leaf Plot
To generate a stem and leaf plot, click on the red triangle for the variable and select Stem and Leaf.
Tips:
· A key to interpret the values is at the bottom of the plot. The top value in this example is 4300, the bottom value is 1700 (values have been rounded to the nearest 100).
· Click on values in the stem and leaf plot to select observations in both the histogram and the data table. Or, select bars in the histogram to select values in the stem and leaf plot and data table.
jmp.com/learn rev 07/2012
Use to display the distribution of continuous variables. They are also useful for comparing distributions.
Box Plots – One Variable
1. From the open JMP® data table, select Analyze > Distribution.
2. Click on another continuous variable from Select Columns, and Click Y, Columns (continuous variables have blue triangles).
3. Click OK. An outlier box plot is displayed by default next to the histogram (or above if horizontal layout). To display a quantile box plot, select the option from the red triangle for the variable.
jmp.com/learn rev 07/2012
Box Plots
The lines on the Quantile Box Plot correspond to the quantiles in the distribut.
MATH 533 RANK Lessons in Excellence-- math533rank.com
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Mb0040 statistics for management
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MATH 533 RANK Achievement Education--math533rank.com
This document outlines the contents of the MATH 533 Entire Course from www.math533rank.com. It includes homework, quizzes, discussion questions and projects for each of the 7 weeks, as well as two final exam sets. The course covers topics such as descriptive statistics, probability, confidence intervals, hypothesis testing, regression and correlation.
MATH 533 RANK Redefined Education--math533rank.com
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BPSC-105 important questions for june term end exam
BPSC-105 important questions for june term end exam
Level 3 NCEA - NZ: A Nation In the Making 1872 - 1900 SML.ppt
Level 3 NCEA - NZ: A Nation In the Making 1872 - 1900 SML.ppt
CapTechTalks Webinar Slides June 2024 Donovan Wright.pptx
CapTechTalks Webinar Slides June 2024 Donovan Wright.pptx
Dealing with heteroscedasticity additional material 2
- 1. Dealing with heteroscedasticity Click Quick and select Estimate Equation. A dialog box will appear as below:- Type dependent variable (gdp) followed by constant (c) and independent variables (invest and unemp) in the space provided. Click ok and the results will be as below:-
- 2. Click View and select Actual, Fitted Residual and direct to Residual Graph The illustration of residual graph will be as below:-(Actual GDP-Predicted GDP)
- 3. Create a new series, residual3 that can capture the values of residuals Genr residual3=resid Click Quick and select Graph. A dialog box will appear as below: Type gdp followed by residuals3 in the provided space Click ok .A dialog box will appear as below: Select Scatter in the specific box and choose Regression Line as a type of Fit Line, and then click ok.
- 4. The illustration of scatter plot will be shown as below:- Click View and select Residual Tests, and then direct to Heteroskedasticity Tests. A dialog box on Heteroskedasticity Tests will appear as below:-
- 5. Select Breusch-Pagan Godfrey.Click ok and the results will be as below:- Null hypothesis : There is no heteroscedasticity (Homoscedasticity) Alternative hypothesis: There is a heteroscedasticity p-value=0.0020, p-value<0.05, Existence of heteroscedasticity Click View and select Residual Tests, and then direct to Heteroskedasticity Tests. A dialog box on Heteroskedasticity Tests will appear
- 6. Select White. Click Ok and the results will be as below:- Null hypothesis : There is no heteroscedasticity (Homoscedasticity) Alternative hypothesis: There is a heteroscedasticity p-value=0.00, p-value<0.05, Existence of heteroscedasticity