{"id":74,"date":"2018-06-05T23:29:00","date_gmt":"2018-06-05T21:29:00","guid":{"rendered":"https:\/\/kindsonthegenius.com\/blog\/2018\/06\/05\/advanced-statistics-quiz-8-concepts-from-multivariate-linear-regression\/"},"modified":"2020-08-22T14:56:06","modified_gmt":"2020-08-22T12:56:06","slug":"advanced-statistics-quiz-8-concepts-from-multivariate-linear-regression","status":"publish","type":"post","link":"https:\/\/kindsonthegenius.com\/blog\/advanced-statistics-quiz-8-concepts-from-multivariate-linear-regression\/","title":{"rendered":"Advanced Statistics Quiz 8 – Concepts from Multivariate Linear Regression"},"content":{"rendered":"
Hello, good to see you!<\/div>\n
I made this post to help you prepare for oral and written quiz or exam on advanced or mathematical statistics.<\/div>\n
<\/div>\n
So basically, I would be explaining the concepts in very easy to understand way to help you understand it and be able to answer in your own words.<\/div>\n

 <\/p>\n

Question 1: What is Partial F-Test and when is it applied<\/b><\/div>\n
Partial F-Test is a statistical test used to in multivariate linear regression where extra variables have been included, to determing whether the extra variables\u00a0 provide enough extra explanatory power as a group.<\/div>\n
<\/div>\n
It is used when the simultaneous test of the statistical significance of a group of variables is being tested and requires two regression models.<\/div>\n

 <\/p>\n

Question 2: Outline and Expain the 3 Modelling Algorithms<\/b><\/div>\n
The three modelling algorithms are:<\/div>\n
    \n
  • Forward Selection<\/li>\n
  • Backward Selection<\/li>\n
  • Stepwise Selection<\/li>\n<\/ul>\n

     <\/p>\n

    Foward Selection<\/i><\/div>\n
    Step 1: In the first step of this algorithm, a list of independent variables with the highest correlation coefficient in the absolute value with the target variable is selected.<\/div>\n
    Then calculate the F-statistic to see if a very strong linear relationship exists between the variables.<\/div>\n

     <\/p>\n

    If there is a strong relationship, then stop, else go to step 1<\/div>\n
    Step 2: In the second step, take the next variable, the highest partial correlation coefficient among the residues with the target variable.. Then calculate Fchange, the extended linear regression. If the calculated value, shows a strong relationship stop, else repeat the process<\/div>\n

     <\/p>\n

    Backward Elimination<\/i><\/div>\n
    This algorithm works in opposite direction to the Foward Selection. In this case, we start by including all the variables from the start, then we select the least suitable ones. Then we calculate the error. Based on the error value, we remove or eliminate the least suitable variables from the selection. We repeat the caculation until the error is at a minimum value.<\/div>\n

     <\/p>\n

    Stepwise Selection<\/i><\/div>\n
    This algorithm is a combination of the Foward Selection and Backward Elimination. This involves gradually removing variables fromthe list of independent variables repeatadly. The stop rule now has a minimum and maximum value. We stop when the F statistic has reached a significant level.<\/div>\n

     <\/p>\n

    Question 3: What is Adjusted Coefficient of Determination R2<\/sup>and What is it Used For?\u00a0 What is the difference between R2<\/sup>and Adjusted R2<\/sup>?<\/b><\/div>\n
    The Adjusted Coefficient of Determination is used in multiple regression to determine how well a multiple regression equation fits the sample data.<\/div>\n
    The main difference between R2<\/sup>\u00a0and adjusted R2<\/sup>\u00a0is that R2<\/sup>increases automatically as new independent variables are added to the regression equation(even if they don\u2019t contribute to the explanatory power of the equation)<\/div>\n
    However, the adjusted R2<\/sup>\u00a0increases only if the added new independent variables contribute to the explanatory power of the regression equation. Therefore, the adjusted R2<\/sup>\u00a0is mor useful measure of regression fit than just the R2<\/sup>.<\/div>\n

     <\/p>\n

    Question 4: What is Heteroscedasticity?<\/b><\/div>\n
    Heteroscedasticity is a concept in regression that means unequal scatter. It is a systematic\u00a0 variation is the spread of the residues\u00a0 oeer the change of measured values.Remember that residue is the errror measured between the regression line and the data point. It is the opposit of homoscedasticity(which means constant variation in the residues)<\/div>\n

     <\/p>\n

    Question 5: What are the Type of Residues<\/b><\/div>\n
    Common Residual<\/div>\n
    Deleted Residual<\/div>\n
    Standardized Residual<\/div>\n
    Studendized Residual<\/div>\n

     <\/p>\n

    Question 6: What is Covariance Ratio?<\/b>
    \nThe coveriance ratio is given by:
    \nCovR = CovTL\/CovTLj
    \nwhere:
    \nCovTL is the covariance between the target variable and the linear regression
    \nCovTLj is the covariance betweent the target variable and teh linear regression gotten by omitting the jth case.<\/div>\n

     <\/p>\n

    Question 7: What is Multicollinearity in Regression?<\/b>
    \nMulticolinearity means the linear correlation relationship between the two or more explanatory variables.<\/div>\n
    \n

     <\/p>\n

    Question 8: Mention some problems caused by Multicollinearity?<\/b><\/p>\n

      \n
    • the effect of the explanatory variables on the depended variables cannot really be separated<\/li>\n
    • the explanatory variables can assume the role of other\u00a0 explanatory variables<\/li>\n
    • estimation of regression coefficients becomes unreliable<\/li>\n
    • in extreme situations, analysis cannot be performed on the data<\/li>\n<\/ul>\n<\/div>\n

       <\/p>\n

      We continue with the next part. You can ask a question in the box below or in the form by the left of this page.<\/div>\n
      <\/div>\n
      Thank you!<\/div>\n","protected":false},"excerpt":{"rendered":"

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