SUMMARY 1 BAD 376 PROBLEM ANALYSIS: REGRESSION ANALYSIS Consider the following simple linear regression: Y-B+BX, Objective: the objective is to use a sample to estimate B. and ẞ, .To do that, we use Ordinary Least Squares Method (OLS). This is how to estimate ẞ, and ẞ, using Ordinary Least Squares Method: Step 1: compute the mean of X and the mean of Y; that is X and Y Step 2: compute the variance of X; that is, VAR(X) Step 3: compute the covariance between X and Y; that is, COV(X, Y) Step 4: compute B, using this formula: COV( X,Y) VAR( X ) Step 5: compute B, using this formula: B₁ =Y-B₁xX The coefficient of Determination (R²) QUESTION 1: R² B₁XCOV( X,Y) VAR( Y ) The following table contains data on X and Y: X₁ Y₁ 3 6 5 4 7 2 Consider the following regression line: Y =ẞ₁ +B,X. 1. Use Ordinary Least Squares Method to estimate B. and B,; 2. Find the prediction line; 3. Compute R². SUMMARY 2 Consider the following simple regression: Ý, B, +‚ׂ. = To conduct the statistical test that the slope is equal to zero, that is, B₁ = 0, involves the following steps: Step1: The null Hypothesis Ho: B₁ = 0 Step 2: The alternative Hypothesis HA: B₁ #0 Step 3: T-statistic: =- B₁-0 SE Where, is the estimate of B SE: the standard error Step 4: Decision criteria. To decide whether to reject Ho or not you need to compare the absolute value of t (t) with taz Where: 1. If > 2. If t
SUMMARY 1 BAD 376 PROBLEM ANALYSIS: REGRESSION ANALYSIS Consider the following simple linear regression: Y-B+BX, Objective: the objective is to use a sample to estimate B. and ẞ, .To do that, we use Ordinary Least Squares Method (OLS). This is how to estimate ẞ, and ẞ, using Ordinary Least Squares Method: Step 1: compute the mean of X and the mean of Y; that is X and Y Step 2: compute the variance of X; that is, VAR(X) Step 3: compute the covariance between X and Y; that is, COV(X, Y) Step 4: compute B, using this formula: COV( X,Y) VAR( X ) Step 5: compute B, using this formula: B₁ =Y-B₁xX The coefficient of Determination (R²) QUESTION 1: R² B₁XCOV( X,Y) VAR( Y ) The following table contains data on X and Y: X₁ Y₁ 3 6 5 4 7 2 Consider the following regression line: Y =ẞ₁ +B,X. 1. Use Ordinary Least Squares Method to estimate B. and B,; 2. Find the prediction line; 3. Compute R². SUMMARY 2 Consider the following simple regression: Ý, B, +‚ׂ. = To conduct the statistical test that the slope is equal to zero, that is, B₁ = 0, involves the following steps: Step1: The null Hypothesis Ho: B₁ = 0 Step 2: The alternative Hypothesis HA: B₁ #0 Step 3: T-statistic: =- B₁-0 SE Where, is the estimate of B SE: the standard error Step 4: Decision criteria. To decide whether to reject Ho or not you need to compare the absolute value of t (t) with taz Where: 1. If > 2. If t
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:SUMMARY 1
BAD 376
PROBLEM ANALYSIS: REGRESSION ANALYSIS
Consider the following simple linear regression:
Y-B+BX,
Objective: the objective is to use a sample to estimate B. and ẞ, .To do that, we use Ordinary
Least Squares Method (OLS).
This is how to estimate ẞ, and ẞ, using Ordinary Least Squares Method:
Step 1: compute the mean of X and the mean of Y; that is X and Y
Step 2: compute the variance of X; that is, VAR(X)
Step 3: compute the covariance between X and Y; that is, COV(X, Y)
Step 4: compute B, using this formula:
COV( X,Y)
VAR( X )
Step 5: compute B, using this formula:
B₁ =Y-B₁xX
The coefficient of Determination (R²)
QUESTION 1:
R²
B₁XCOV( X,Y)
VAR( Y )
The following table contains data on X and Y:
X₁
Y₁
3
6
5
4
7
2
Consider the following regression line: Y =ẞ₁ +B,X.
1. Use Ordinary Least Squares Method to estimate B. and B,;
2. Find the prediction line;
3. Compute R².
Transcribed Image Text:SUMMARY 2
Consider the following simple regression: Ý, B, +‚ׂ.
=
To conduct the statistical test that the slope is equal to zero, that is, B₁ = 0, involves the
following steps:
Step1: The null Hypothesis Ho: B₁ = 0
Step 2: The alternative Hypothesis HA: B₁ #0
Step 3: T-statistic: =-
B₁-0
SE
Where, is the estimate of B
SE: the standard error
Step 4: Decision criteria. To decide whether to reject Ho or not you need to compare the
absolute value of t (t) with taz
Where:
1. If
>
2. If t<t
we reject the null hypothesis, Ho.
a/2
we do not reject the null hypothesis, Ho.
a: The error level or the significance level (the significance levels commonly used
are: 1%, 5%, and 10%)
ta: The critical value.
The degrees of freedom (DF): DF-n- (the number of the coefficients in the
regression)
Note: for a simple linear regression involving 2 coefficients, DF = n -2
QUESTION 2:
Consider the following simple linear regression, Q = B₁+B₁₁₁. Test whether is equal to zero
against the alternative that B is not equal to zero. Assume that the standard error (SE) is 3, the
OLS estimate of B is 6 and the sample size is 17 (n=17). Use a=10%.
2
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