{"id":48551,"date":"2024-04-15T22:42:55","date_gmt":"2024-04-15T22:42:55","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=48551"},"modified":"2024-04-15T22:42:55","modified_gmt":"2024-04-15T22:42:55","slug":"which-of-the-following-assumptions-do-we-make-while-deriving-linear-regression-parameters-1-the-true-relationship-between-dependent-y-and-predictor-x-is-linear-2-the-model-errors-are-statistically","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/which-of-the-following-assumptions-do-we-make-while-deriving-linear-regression-parameters-1-the-true-relationship-between-dependent-y-and-predictor-x-is-linear-2-the-model-errors-are-statistically\/","title":{"rendered":"Which of the following assumptions do we make while deriving linear regression parameters? 1. The true relationship between dependent y and predictor x is linear 2. The model errors are statistically independent 3. The errors are normally distributed with a 0 mean and constant standard deviation 4. The predictor x is non-stochastic and is measured error-free"},"content":{"rendered":"

[amp_mcq option1=”1, 2 and 3″ option2=”1,3 and 4″ option3=”1 and 3″ option4=”All of above” correct=”option4″]<\/p>\n

The correct answer is D. All of the above.<\/p>\n

The assumptions of linear regression are:<\/p>\n

    \n
  1. The true relationship between dependent $y$ and predictor $x$ is linear. This means that the line of best fit is the best way to represent the data.<\/li>\n
  2. The model errors are statistically independent. This means that the errors are not correlated with each other.<\/li>\n
  3. The errors are normally distributed with a 0 mean and constant standard deviation. This means that the errors are evenly distributed around the line of best fit, with a mean of 0 and a constant standard deviation.<\/li>\n
  4. The predictor $x$ is non-stochastic and is measured error-free. This means that the predictor is not random and is measured without error.<\/li>\n<\/ol>\n

    If any of these assumptions are violated, the results of the linear regression may not be accurate. For example, if the true relationship between $y$ and $x$ is not linear, the line of best fit will not be the best way to represent the data. If the errors are correlated with each other, the standard errors of the coefficients will be underestimated. If the errors are not normally distributed, the t-tests and F-tests may not be accurate. If the predictor $x$ is random or is measured with error, the coefficients will be biased.<\/p>\n

    It is important to check the assumptions of linear regression before using the results. There are a number of ways to do this, including looking at the residuals, the normality plot, and the Cook’s distance. If any of the assumptions are violated, you may need to transform the data or use a different statistical method.<\/p>\n","protected":false},"excerpt":{"rendered":"

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