Based on a sample of n = 28, the least-squares method was used to develop the prediction line ₁ = 8 + 3X₁. In addition, Syx = 2.3, X = 7, and Σ (x₁ - x)² = 28. Complete parts (a) through (c) below. i=1 a. Construct a 90% confidence interval estimate of the population mean response for X= 5. SHY|X=5³ (Round to two decimal places as needed.) b. Construct a 90% prediction interval of an individual response for X = 5. ≤YX=5³ (Round to two decimal places as needed.) c. Compare the results of (a) and (b) with those for X= 7, which are 28.26 ≤ Hy|x=7 ≤29.74 and 25.01 ≤Yx=732.99. Which intervals are wider? Why? the mean X. The intervals for X= ▼are wider because X = 7 is

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Based on a sample of n = 28, the least-squares method was used to develop the prediction line Ŷ, = 8 +3X;. In addition, Syx = 2.3, X= 7, and Σ (X₁-X)² = 28. Complete parts (a) through (c) below.
i=1
a. Construct a 90% confidence interval estimate of the population mean response for X = 5.
≤Hy|x=5³
(Round to two decimal places as needed.)
b. Construct a 90% prediction interval of an individual response for X = 5.
≤YX=5³
(Round to two decimal places as needed.)
c. Compare the results of (a) and (b) with those for X= 7, which are 28.26 HyX=7 ≤29.74 and 25.01 ≤Yx=732.99. Which intervals are wider? Why?
▼the mean X.
The intervals for X =
C
▼are wider because X = 7 is
Transcribed Image Text:Based on a sample of n = 28, the least-squares method was used to develop the prediction line Ŷ, = 8 +3X;. In addition, Syx = 2.3, X= 7, and Σ (X₁-X)² = 28. Complete parts (a) through (c) below. i=1 a. Construct a 90% confidence interval estimate of the population mean response for X = 5. ≤Hy|x=5³ (Round to two decimal places as needed.) b. Construct a 90% prediction interval of an individual response for X = 5. ≤YX=5³ (Round to two decimal places as needed.) c. Compare the results of (a) and (b) with those for X= 7, which are 28.26 HyX=7 ≤29.74 and 25.01 ≤Yx=732.99. Which intervals are wider? Why? ▼the mean X. The intervals for X = C ▼are wider because X = 7 is
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