Log in
HomeClass Notes1,200,000AU40,000

STAT3012 Lecture Notes - Lecture 10: Semiparametric Regression, Box Plot, Google

22 views25 pages
School
University of Sydney
Department
Statistics
Course
STAT3012
Professor
Michael

For unlimited access to Class Notes, a Class+ subscription is required.

Lecture 10 - Variable selection: Backward and forward
New concepts
✷Backward variable selection
✷The drop1 and update command
✷Forward variable selection
✷The add1 command
Applied Linear Models: Lecture 10 1
find more resources at oneclass.com
find more resources at oneclass.com
Unlock document

This preview shows pages 1-3 of the document.
Unlock all 25 pages and 3 million more documents.

Already have an account? Log in
New topic – Variable selection
Motivation
✷Hypotheses testing:
Aims to test for redundancy/non-redundancy of
◦single explanatory variables and
◦groups of explanatory variables.
Reason: Wanting to test hypotheses about a given group of covariates.
✷Statistical learning:
What is the ‘best’ group of explanatory variables for describing and/or predicting
the response?
Applied Linear Models: Lecture 10 2
find more resources at oneclass.com
find more resources at oneclass.com
Unlock document

This preview shows pages 1-3 of the document.
Unlock all 25 pages and 3 million more documents.

Already have an account? Log in
Theory – Possible subsets
✷Let mdenote any subset of pmdistinct elements from {1, . . . , p}.
Remark: Typically the intercept is forced to be part of the model.
✷Let Mdenote a set of linear regression models for the relationship between Y
and X.
Remark: Often Mis reduced by preselection.
Example – Three explanatory variables (k= 3)
✷There are 24= 16 distinct subsets of {1,2,3,4}:∅,{1},{2},{1,2},{3},. . .,
{1,2,3,4}.
✷If the intercept is forced to be be part of the model, then there are 24−1= 2k= 8
possible subsets.
Applied Linear Models: Lecture 10 3
find more resources at oneclass.com
find more resources at oneclass.com
Unlock document

This preview shows pages 1-3 of the document.
Unlock all 25 pages and 3 million more documents.

Already have an account? Log in

Document Summary

Lecture 10 - variable selection: backward and forward. Aims to test for redundancy/non-redundancy of: single explanatory variables and, groups of explanatory variables. Reason: wanting to test hypotheses about a given group of covariates. Let m denote any subset of pm distinct elements from {1, . Remark: typically the intercept is forced to be part of the model. Let m denote a set of linear regression models for the relationship between y and x. Example three explanatory variables (k = 3) There are 24 = 16 distinct subsets of {1, 2, 3, 4}: , {1}, {2}, {1, 2}, {3}, . If the intercept is forced to be be part of the model, then there are 24 1 = 2k = 8 possible subsets. For simplicity we use m as an abbreviation for the linear regression model of y on those columns of x indexed by m. The linear regression model m is given by yi = 0 + x.

Get access

Grade+
$40 USD/m
Billed monthly
Grade+
Homework Help
Study Guides
Textbook Solutions
Class Notes
Textbook Notes
Booster Class
10 Verified Answers
Class+
$30 USD/m
Billed monthly
Class+
Homework Help
Study Guides
Textbook Solutions
Class Notes
Textbook Notes
Booster Class
7 Verified Answers

Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related Documents

STAT3012 Lecture Notes - Lecture 11: Gross Domestic Product, Feature Selection, Stepwise Regression
grayprairie-dog236
STAT3012 Lecture Notes - Lecture 12: Numerical Stability, Simple Linear Regression, Correlation And Dependence
grayprairie-dog236
STAT3012 Lecture Notes - Lecture 5: Standard Deviation, Forb, Sampling Distribution
grayprairie-dog236

Related Questions

Multiple Choice

1. You have a large dataset that will print on several pages. You want to ensure that related records print on the same page with column and row labels visible and that confidential information is not printed. You should apply all of the following page setup options except which one to accomplish this task?

(a) Set a print area.

(b) Print titles.

(c) Adjust page breaks.

(d) Change the print page order.

2. You are working with a large worksheet. Your row headings are in column A. Which command(s) should be used to see the row headings and the distant information in columns X, Y, and 2?

(a) Freeze Panes command

(b) Hide Rows command

(c) New Window command and cascade the windows

(d) Split Rows command

3. Which statement is not a recommended guideline for designing and creating an Excel table?

(a) Avoid naming two fields with the same name.

(b) Ensure that no blank columns separate data columns within the table.

(c)-Leave one blank row between records in the table.

(d) Include field names on the first row of the table.

4. Which of the following characters are wildcards in Excel? (Check all that apply.)

(a) *

(b) #

(e) ?

(d) $

5. What should you do to ensure that records in a table are unique?

(a) Do nothing; a logical reason probably exist to keep identical records.

(b) Use the remove duplicates command.

(c) Look at each row yourself and manually delete duplicate records.

(d) Find the duplicate records and change some of the data to be different

6. Which Conditional Formatting rule is best suited to apply formatting to the top five values in a range of values?

(a) Above Average

(b) Greater Than

(c). Top 10 Items

(d) Between

7. Which date filter option enables you to restrict the view to only dates that occur in March of 2018?

(a) Equals

(b) Before

(c) After

(d) Between

8. Which of the following is an unqualified structured reference?

(a) =[Purchase_Price]-[Down Payment]

(b) =Sales[Purchase_Price]-Sales[Down_Payment]

(c) =Purchase Price-Down_Payment

(d) =[Sales]Purchase_Price [Sales]Down_Payment

 

9. Which of the following is not an aggregate function that can be applied in a total row?

(a) MAX

(b) AVERAGE

(c) COUNT

(d) VLOOKUP

 

10. If you would like to set a conditional formatting rule based on the function=AND(G6"Finance". H7<7000), which formatting rule type is needed?

(a) Format all cells based on their values

(b) Format only cells that contain

(c) use formula to determine which cells to format

(d) Format only values that are above or below average

(14 marks) Fortune magazine publishes a list of the world’s billionaires each year. We will examine the top 97 of the 1992 list. Their wealth, age, and geographic location (Asia, Europe, Middle East, United States, and Other) are reported. Wealth is a right-skewed variable, so we will consider the natural logarithm log wealth to be the response and will see if age and geographic location are predictors.
(a) (2 marks) Let
Ebe a variable that is 1 if the person is from Europe and 0 otherwise,
Mbe a variable that is 1 if the person is from the Middle East and 0 otherwise,
Obe a variable that is 1 if the person is from the “Other” region and 0 otherwise,
and
Ube a variable that is 1 if the person is from the United States and 0 otherwise.
State a linear model for the mean of log wealth that includes age and the above 4
geographic variables. Call this the full model.
(b) (5 marks) The SSY for these data is 28.3351 and the SSE from fitting the full model
is 27.0461. Use this information to construct an ANOVA table. Your table should
include columns for Source, df, SS, MS and F, and should include rows for the model
(full model), residual and total.
(c) (2 marks) In addition to the full model, the reduced model that includes only an
intercept and age is fit. What is the null hypothesis being considered by fitting these
two models? (Refer to quantities defined in your model.)
(d) (3 marks) The SSM from the reduced model is 59.7. Calculate an F-statistic to test the hypothesis of part (c). State the degrees of freedom for the F-distribution
you would compare this statistic to. (You do not need to calculate the p-value or actually test the hypothesis.)
(e) (1 mark) Using terminology from class, name the kind of Ftest that the statistic in part (d) corresponds to.
(f) (1 mark) If the null model for these data is compared to the model that includes an
intercept and age, what are the results?
1.Create a list that contains 10 successive integers starting with the value in the variable start. For example, if start is 7, the resulting list should be [7, 8, 9, 10, 11, 12, 13, 14, 15, 16]. Store the list in a variable named my_list. Assume that the value of start has already been set.
 
2.Create a list that is made up of the first half of the elements of a list called original_list. Store the new list in a variable called half_list. Assume that the original list has already been initialized and contains an even number of elements.
 
 
3. Write a predicate function called same_ends that accepts a list of integers and an integer (n) as arguments. Return True if the first n numbers in the list are the same as the last n numbers in the list, and False otherwise. For example, if the list was [1, 2, 3, 4, 99, 1, 2, 3, 4], the function would return True if n is 4 and False if n is 3. Assume that n is between 1 and the length of the list, inclusive.
 
4.Write a function called highest_values that accepts as arguments a list of numeric values and a single integer (n). The function should return a list made up of the largest n values from the argument list in order from lowest to highest. For example, if the argument list is [46, 82, 25, 61, 70, 33, 54] and n is 3, the return value should be [61, 70, 82]. Assume that the argument list contains at least n elements.
 
5.Assume that a list of integers stored in a variable named original contains exactly two elements that are zero. Write code that creates a separate list that contains the elements from original that are between the two zeros. Do not include the zeros in the new list. Store the list in a variable named between_zeros.
 
6. Write a function called price_range that accepts a list of floating-point numbers representing prices as an argument and returns the the difference between the highest price and the lowest price. Do NOT use the built-in functions max or min in your solution. Assume that all prices are positive values and that none of them exceed 10,000.00.
 
7. Write a function called count_vowels that accepts a string argument that represents a word and returns the number of vowels that are in the word. The vowels are A, E, I, O, and U (ignore the 'sometimes Y' rule). Count both uppercase and lowercase vowels.
 
8.
Assume that the variable table holds a two-dimensional list of integers. Write code that computes the sum of all elements in the table, assigning the result to the variable table_sum.