Suppose your friend Paolo needs your assistance testing five exclusion restrictions in a multiple linear regression model at the 95% level. Specificaly his null hypothesis is that Be ., Bo are all equal to 0, after controlling for the independent variables z1 , Is. The original, unrestricted model consisted of 10 population slope parameters, Bi ., Bo, plus an intercept parameter Bo and was estimated using a random sample of 470 observations. You ask Paolo for the residual sum of squares from the restricted and unrestricted models. He says he lost those figures, but he did save the R- squared values. The R-squared for the unrestricted model is 0.911, while the R-squared for the restricted model is 0.892. Since the unrestricted model has | degrees of freedom, while the restricted model has | degrees of freedom, you know that the number of excdusion restrictions must be q=| fail to reject Note: The critical value for the F-distribution, at the 95% level, is 2.6. reject After computing the F-statistic, you advise Paolo that because the F-statistic is he should the null hypothesis that Be ., Bro are jointly insignificant.

Suppose your friend Paolo needs your assistance testing five exclusion restrictions in a multiple linear regression model at the 95% level. Specificaly his null hypothesis is that Be ., Bo are all equal to 0, after controlling for the independent variables z1 , Is. The original, unrestricted model consisted of 10 population slope parameters, Bi ., Bo, plus an intercept parameter Bo and was estimated using a random sample of 470 observations. You ask Paolo for the residual sum of squares from the restricted and unrestricted models. He says he lost those figures, but he did save the R- squared values. The R-squared for the unrestricted model is 0.911, while the R-squared for the restricted model is 0.892. Since the unrestricted model has | degrees of freedom, while the restricted model has | degrees of freedom, you know that the number of excdusion restrictions must be q=| fail to reject Note: The critical value for the F-distribution, at the 95% level, is 2.6. reject After computing the F-statistic, you advise Paolo that because the F-statistic is he should the null hypothesis that Be ., Bro are jointly insignificant.

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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Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

### 11. Testing Multiple Exclusion Restrictions with the F-Test and R-Squared Figures

Suppose your friend Paolo needs your assistance testing five exclusion restrictions in a multiple linear regression model at the 95% level. Specifically, his null hypothesis is that $ \beta_6 , \ldots, \beta_{10} $ are all equal to 0, after controlling for the independent variables $ x_1 , \ldots, x_5 $. The original, unrestricted model consisted of 10 population slope parameters, $ \beta_1 , \ldots, \beta_{10} $, plus an intercept parameter $ \beta_0 $ and was estimated using a random sample of 470 observations.

You ask Paolo for the residual sum of squares from the restricted and unrestricted models. He says he lost those figures, but he did save the R-squared values. The R-squared for the unrestricted model is 0.911, while the R-squared for the restricted model is 0.892.

Since the unrestricted model has $ \_\_\_\_\_\_\_ $ degrees of freedom, while the restricted model has $ \_\_\_\_\_\_\_ $ degrees of freedom, you know that the number of exclusion restrictions must be $ q = (\_\_\_\_\_\_\_) $.

- **Note:** The critical value for the F-distribution, at the 95% level, is 2.6.

After computing the F-statistic, you advise Paolo that because the F-statistic is $ \_\_\_\_\_\_\_ $, he should $ \_\_\_\_\_\_\_ $ the null hypothesis that $ \beta_6, \ldots, \beta_{10} $ are jointly insignificant.

#### Diagram Explanation:

The diagram contains a decision box with two choices for Paolo:
- **Fail to Reject** (located on the left side of the box)
- **Reject** (located on the right side of the box)

The diagram is positioned to indicate that Paolo needs to make a decision based on the computed F-statistic in relation to the critical value.
- If the F-statistic is greater than 2.6, Paolo should "Reject" the null hypothesis, implying that the restrictions are not jointly insignificant.
- If the F-statistic is less than or equal to 2.6, Paolo should "Fail to Reject" the null hypothesis, implying

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