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StatTutor Lesson - Least-squares regression line

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      Questions 1-2

      109

      Question 1.

      What is another name for prediction error?

      A.
      B.
      C.
      D.

      Incorrect. Prediction error is also called “residual.”
      Correct. Prediction error is also called “residual.”
      Incorrect. Try again.
      2

      Questions 3-4

      134

      Question 3.

      Fill in the blank: The least squares regression line has the _____________ sum of squared prediction errors.

      A.
      B.
      C.

      Incorrect. Because we want the best fit of the regression line to the data, we want the “smallest” sum of square residuals.
      Correct. Because we want the best fit of the regression line to the data, we want the “smallest” sum of square residuals.
      Incorrect. Try again.
      2

      Question 5

      154

      Question 5.

      Fill in the blank: The line with the smallest sum of squared residuals has an SSE of ___________.

      A.
      B.
      C.
      D.
      E.

      Incorrect. The smallest SSE given in the table is 55.78.
      Correct. The smallest SSE given in the table is 55.78.
      Incorrect. Try again.
      2

      Applet

      194

      Questions 6-7

      256

      Question 6.

      Fill in the blank: The value of slope, b, depends on _____________.

      A.
      B.
      C.

      Incorrect. Since b=rsysx, the value of slope, b, is computed using “r”.
      Correct. Since b=rsysx, the value of slope, b, is computed using “r”.
      Incorrect. Try again.
      2

      Questions 8-9

      375

      Question 8.

      What is the value of Y when X = 0?

      A.
      B.
      C.
      D.
      E.

      Incorrect. In the equation ŷ = 2.034 + 0.051x, y-intercept is 2.034.
      Correct. In the equation ŷ = 2.034 + 0.051x, y-intercept is 2.034.
      Incorrect. Try again.
      2

      Question 10

      415

      Question 10.

      What is a one-unit increase in X for these data?

      A.
      B.

      Incorrect. X is composite ACT score and ACT scores are measured in points. So, a one-unit increase in X is a one point increase in composite ACT score.
      Correct. X is composite ACT score and ACT scores are measured in points. So, a one-unit increase in X is a one point increase in composite ACT score.
      Incorrect. Try again.
      2

      Questions 11-13

      462

      Question 11.

      Do you think this y-intercept is a meaningful number?

      A.
      B.

      Incorrect. Predicting a graduating GPA of 2.034 for a zero composite ACT score is ludicrous.
      Correct. Predicting a graduating GPA of 2.034 for a zero composite ACT score is ludicrous.
      Incorrect. Try again.
      2