Welcome to Econ 420 Applied Regression Analysis

Study GuideWeek Four

Ending Wednesday, September 19(Assignment 4 which is included in this study

guide is due before Wednesday, September 19 at 10:00 PM)

Notes

• Exam 1– Thursday, September 27 at 8:00 A.M. in

Thomas 223 – Covers Chapters 1, 2, and 3

• Assignment 3– Will be grades and emailed to you soon

Answer Key to Assignment 2:Here is how your EViews output should look.• Dependent Variable: W• Method: Least Squares• Date: XX/XX/07 • Time: XX:XX• Sample: 1 8• Included observations: 8• Variable Coefficient Std. Error t-Statistic Prob.

C - 231.1391 92.54581 -2.497565 0.0467 H 5.879205 1.314659 4.472039 0.0042R-squared 0.769223 Mean dependent var 181.8750Adjusted R-squared 0.730760 S.D. dependent var 32.39681S.E. of regression 16.81016 Akaike info criterion 8.694162Sum squared resid 1695.489 Schwarz criterion 8.714023Log likelihood -32.77665 F-statistic 19.99913Durbin-Watson stat 1.128086 Prob(F-statistic) 0.004228

What you should have recognized.

1. Coefficient value -231.1391 represents the W intercept (when H = 0) of the regression equation.

2. Coefficient value 5.879205 represents the slope of the estimated regression line (the value of W increases by 5.879205 when the Value of H increases by 1 inch, ignoring the effect of other variables on W.

3. The mean of the dependant variable value weight is 181.8750= the average weigh value of the 8 observations

4. The standard deviation of the dependent variable value 32.39681 is the average weight distance of the observations away from the mean.

5. The sum of the squared residuals = 1695.489 = is the sum of the squared differences between the predicted Ws and the actual (See Equation 1-8 on Page 12)

What you could not recognize

• Everything else on the output.

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.

Two Sided Hypotheses

• Suppose all you want to show is that something affects something else. But you don’t want to show the direction of the relationship

• In this case, you will set a two sided hypothesis

• Example – All you want to show is that calorie intake does

affect the weight.– In this case you would set up a two sided test.

Suppose B3 is the true coefficient of calorie intake, then the two sided hypothesis looks like this

You expect to

• Reject the null hypothesis H0 in favor of alternative hypothesis, HA

• 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.

One sided hypotheses

• Suppose you want to show that something has a positive (or negative) effect on something else. In this case, you will set a one sided hypothesis

• Example – you want to show that calorie intake affect the

weight in a positive way– In this case you would set up a one sided test

Suppose B3 is the true coefficient of calorie intake, then the one sided hypothesis looks like this

–H0: B3 ≤0

–HA: B3 >0

You expect to

• Reject the null hypothesis H0 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 I Errors

• Refers to rejecting a true null hypothesis• Example• Weight = ……..+ B3 calorie in take + error

–H0: B3 ≤0–HA: B3 >0

• If you reject a true H0, you will conclude that the higher the calorie intake the higher the weight; while in reality, calorie intake does not matter.

Type II Error

• Refers to failing to reject a false null hypothesis• Example• Weight = ……..+ B3 calorie in take + error

–H0: B3 ≤0

–HA: B3 >0

• If you fail to reject a false H0, you will conclude that calorie intake does not matter; while in reality, it does.

Type I/Type II Errors

B3 is zero or negative

B3 is positive

We conclude that B3 is positive

Type I error No error

We conclude that B3 is zero or negative

No error Type II error

Which type of error is more serious?

• –   Type I error: We conclude that the higher calorie in take, the height the weight. (While in reality there is no correlation between the two.) So we put a lot of effort into watching our calorie intake while we should not.

• –   Type II error: We conclude that calorie intake does not affect the weight, while it actually does. So, we do not watch our diet. (no effort)

• –   When testing hypothesis we try to minimize type I 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-1

• 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

• Step Three

• Estimate the regression equation and find the t- statistic

• Formula (Page 48)

• T-stat. for the null hypothesis equal to zero is reported by EViews.

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 (= 0. ≥0 or ≤0 ]}

2. #3, Page 613. # 8, Page 62