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Hypothesis Testing - Applied Regression Analysis - Lecture Slides, Slides of Data Analysis & Statistical Methods

Alliance UniversityData Analysis & Statistical Methods

It is the Lecture Slides of Applied Regression Analysis which includes Perfect Multicollinearity, Overall Significance of Equation, Recap, Population of Students etc. Key important points are: Hypothesis Testing, Collect a Sample, Estimate the Coefficients, Conclusion, Population Coefficient, Alternative Hypothesis, Sense or Theory, Expect to Reject, Relationship, Hypothesis

Typology: Slides

2012/2013

Uploaded on 02/07/2013

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Hypothesis Testing (Chapter 3,
up to page 53)
•Remember we don’t see the true line
–So we don’t know the true intercept or the
slope coefficients.
•We collect a sample.
•We use OLS to estimate the coefficients.
•Hypothesis testing refers to using sample
information to draw a conclusion about the
true population coefficient .
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Hypothesis Testing (Chapter 3,

up to page 53)

  • Remember we don’t see the true line
    • So we don’t know the true intercept or the slope coefficients.
  • We collect a sample.
  • We use OLS to estimate the coefficients.
  • Hypothesis testing refers to using sample

information to draw a conclusion about the

true population coefficient.

Four Steps of Hypothesis

Testing

Step One

  • Set the null and alternative hypotheses

about the true coefficients.

  • Alternative hypothesis is consistent with our common sense or theory. It is what we expect to find. It is what we expect to fail to reject.
  • Null hypothesis is what we expect to not find. It is what we expect to reject.

Suppose B 3 is the true coefficient

of calorie intake, then the two

sided hypothesis looks like this

You expect to

  • Reject the null hypothesis H 0 in favor of

alternative hypothesis, H A

  • And if you do,
  • You have found empirical evidence that

calorie intake does matter.

  • However, you are not making any

statements with regards to the nature of

the relationship between calorie in take

and weight.

Suppose B 3 is the true coefficient of

calorie intake, then the one sided

hypothesis looks like this

  • H 0 : B3 ≤
  • H (^) A : B 3 >

You expect to

  • Reject the null hypothesis H 0 in favor of alternative hypothesis, HA
  • And if you do,
  • You have found empirical evidence that calorie intakes have a positive effect on weight.
  • Notes
    • A one sided test is stronger than a two sided test.
    • You must test a stronger hypothesis when possible.

Type II Error

  • Refers to failing to reject a false null hypothesis
  • Example
  • Weight = ……..+ B3 calorie in take + error
    • H 0 : B 3 ≤
    • HA: B 3 >
  • If you fail to reject a false H 0 , you will

conclude that calorie intake does not

matter; while in reality, it does.

Type I/Type II Errors

B 3 is zero or negative

B 3 is positive

We conclude that B 3 is positive

Type I error No error

We conclude that B 3 is zero or negative

No error Type II error

Four Steps of Hypothesis

Testing

  • Step Two
  • Choose the level of significance (alpha)
    • Alpha measures the probability of rejecting a true null hypothesis (type I error)
    • The smaller alpha the smaller the probability of type I error
  • Find the critical tc (page 312)
    • Degrees of freedom = n-k-
      • Where n=sample size, k= number of independent variables
  • Formulate the decision rule

The decision rule

Otherwise, fail to reject the null hypothesis; where t = t-statistics

And t- stat is

B^ is the estimated B Bnullis the value of B under null hypothesis (usually zero) SE (B^) is the standard error of B^

Four Steps of Hypothesis

Testing

  • Stop Four
  • Apply the decision rule to either
    • Reject the null hypothesis
    • Or fail to reject the null hypothesis

Assignment 4

(Due before 10 PM on Wednesday, September 19, 30 points)

  1. Set up the appropriate null and alternative hypotheses for our height- weight equation that we estimated before. Test your hypothesis at alpha = 10 percent. Don’t skip any steps. Evaluate your results. {Note: EViews output includes both the stand errors and the t-stats [for null hypotheses that have zero in them (=
    1. ≥0 or ≤0 ]}
  2. #3, Page 61

  3. 8, Page 62