StatTutor Lesson - Conditions for Regression Inference

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StatTutor: Conditions for regression inference
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      Question 1

      92

      Question 1.

      True or false: The values computed previously from the sample data for y-intercept (–36.944) and slope (5.066) are the values for α and β, respectively in the theoretical regression model: µY = α + βX.

      		A.
      		B.
      Correct. µY = α + βX is the theoretical model and the values for y-intercept and slope that we compute from the data are only estimates (statistics) of the parameters α and β, respectively, but not their actual values.
      Incorrect. µY = α + βX is the theoretical model and the values for y-intercept and slope that we compute from the data are only estimates (statistics) of the parameters α and β, respectively, but not their actual values.
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      Question 2

      152

      Question 2.

      True or false: One of the conditions for inference in regression is that the variability of the y’s about the regression line is constant for all x-values.

      		A.
      		B.
      Correct. This is a true statement. The variability of the y’s is measured by σ.
      Incorrect. This is a true statement. The variability of the y’s is measured by σ.
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      Question 3

      205

      Question 3.

      True or false: In theory, there is a distribution of y values at each x value. And all of these distributions need to have a Normal shape for inference.

      		A.
      		B.
      Correct. This is a true statement.
      Incorrect. This is a true statement.
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      Question 4

      228

      Question 4.

      True or false: For inference in linear regression to be valid, the values of the y’s at one x value must affect the values of the y’s at all other x-values.

      		A.
      		B.
      Correct. The opposite is true. For inference to be valid in regression the y’s at one x value must NOT affect the y values at any other x value.
      Incorrect. The opposite is true. For inference to be valid in regression the y’s at one x value must NOT affect the y values at any other x value.
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      Question 5

      419

      Question 5.

      When is it appropriate to estimate the values of α and β using data in the theoretical µY = α + βX?

      		A.
      		B.
      		C.
      Correct. A least squares line should only be used to model the relationship between X and Y when that relationship is linear.
      Incorrect. A least squares line should only be used to model the relationship between X and Y when that relationship is linear.
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      Question 6

      446

      Question 6.

      What can we expect to see in a scatterplot when the standard deviation of the y’s is not constant for all x values?

      		A.
      		B.
      		C.
      Correct. When the scatter of the points about the line is the same for all x values, standard deviation is constant. However, when the scatter is not the same, but continues to increase (or vice versa), standard deviation is not constant.
      Incorrect. When the scatter of the points about the line is the same for all x values, standard deviation is constant. However, when the scatter is not the same, but continues to increase (or vice versa), standard deviation is not constant.
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      Question 7

      466

      Question 7.

      What of the following is an indicator of non-Normality?

      		A.
      		B.
      		C.
      Correct. Typically, t procedures are robust with respect to Normality provided the data are not strongly skewed and have no outliers. In regression the plot used to check for outliers is a plot of the residuals.
      Incorrect. Typically, t procedures are robust with respect to Normality provided the data are not strongly skewed and have no outliers. In regression the plot used to check for outliers is a plot of the residuals.
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