Suppose we are making predictions of the dependent variable y for specific values of the independent variable x using a simple linear regression model holding the confidence level constant. Let Width (C. I) = the width of the confidence interval for the average value y for a given value of x, and Width (P. I) = the width of the prediction interval for a single value y for a given value of x. Which of the following statements is true?

Question

Mathematics

Hicks

7 October, 15:57

Suppose we are making predictions of the dependent variable y for specific values of the independent variable x using a simple linear regression model holding the confidence level constant. Let Width (C. I) = the width of the confidence interval for the average value y for a given value of x, and Width (P. I) = the width of the prediction interval for a single value y for a given value of x. Which of the following statements is true?

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Mila Cisneros · Answer 1

width (C. I) ∠ width (P. I)

Step-by-step explanation:

In statistics, a confidence interval (C. I) is known as an interval estimate which is computed using the observed data that might contain the actual value of an unknown parameter. The confidence level is commonly used for estimation before examining the actual data. On the other hand, the prediction interval (P. I) is a range of values that calculate the value of a new observation by considering the existing model developed using the actual data. Therefore, the true statement is:

width (C. I) ∠ width (P. I)