By NEAS - 7/2/2024 1:11:19 PM
MS Module 20 Standardized residuals ratio two points practice exam questions
(The attached PDF file has better formatting.)
[The practice problems in the 24 modules explain the statistical procedures; the practice exam questions in this thread shows what you will be asked on the final exam.]
A regression model has the independent variable X values {1, 2, …, 7}.
● At the point x = 3, the residual is 0.16 and the standardized residual is 0.11
● The residual at the point x = 2 is -0.25
Question 20.1:
What is , the average X value?
Answer 20.1: (1 + 7) / 2 = 4
Question 20.2: Sxx
What is Sxx, the sum of squared residuals for the X values?
Answer 20.2: (1 – 4)2 + (2 – 4)2 + (3 – 4)2 + (4 – 4)2 + (5 – 4)2 + (6 – 4)2 + (7 – 4)2 = 28
Question 20.3: Ratio of residual to standardized residual
What is the ratio of the residual to the standardized residual at the point x = 3?
Answer 20.3: 0.16 / 0.11 = 1.455
Question 20.4: Standardized residual factor
At the point x = 3, what is the value of [(1 – 1/n – (xi – )2 / Sxx)]½ ?
Answer 20.4: (1 – 1/7 – (3 – 4)2 / 28)0.5 = 0.906
Question 20.5: Least squares estimate for σ
What is s, the least squares estimate for σ?
Answer 20.5: 1.455 / 0.906 = 1.606
(the standardized residual = the residual / ( σ × [(1 - 1/n - (xi - )2 / Sxx)]½ ) )
Question 20.6: Standardized residual
What is the standardized residual at the point x = 2?
Answer 20.6: -0.25 / (1.606 × (1 – 1 / 7 – (2 – 4)2 / 28)0.5 ) = -0.184
(the standardized residual = the residual / ( σ × [(1 - 1/n - (xi - )2 / Sxx)]½ ) )
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